POA ground reflected albedo

[george]

Hi,

POA ground reflected radiation from your website, has the following formula:

 

Eg = ((GHI x albedo x (1-cos(surfaceTiltAngle))/2)

 

Albedo is defined as a reflection coefficient of a ground surface.

But can it also be a reflection coefficient of a roof surface? A flat roof for example?

What about the sloped roof? If a PV panel is close (flush) roof mounted on a sloped roof (check the attached photo for an example), then an albedo should be albedo of that sloped roof surface? In this example, albedo of red roof tiles (0.33)? Is this correct? Or should I albedo of the ground bellow the roof be used instead?

Thank you for the reply.

Flush mount PV array on red roof tiles

[André Mermoud]

I don't understand what you mean.

The tiles cannot bring any albedo contribution to the PV modules here, as the PV module doesn't "see" them.

In a general way, the albedo is proportionnal to the cosinus of the corresponding incidence angle. Therefore any radiation coming from a surface in the plane of the array will have a null contribution.

On the other hand, the electrical yield of a string of modules is lead by the poorest module (the less irradiated). Therefore for being really efficient, a reflexion should be homogeneous on a whole module string.

[george]

Thank you for the reply Andre.

So in this specific upper case, what is the albedo value that should be taken into account when calculating POA ground reflected radiation? If not the albedo of the red roof tiles, then the albedo of the ground surface below the roof?

[george]

Thank you for the reply Marvin,

I am not in a position to measure anything on the site.

 

What surfaces in the area make up the largest reflective surfaces with highest albedo value?

 

Let's say that next to the house (from the upper photo) is another house with an aluminium roof (albedo for aluminium = 0.85). On the opposite side of the house there is another house with red tiles roof tiles. Below the roofs, grounds of each of these three backyards are covered with grass (albedo approx. 0.20).

Would that mean that this aluminium roof is the largest reflective surface near my roof with PV panels, with the largest value of albedo (0.85)?

I did a little testing:

nameplate 4 kW

azzimuth angle = 180

tilt angle = 45 (Maybe the roof on an upper photo is a bit less, 40, 38 but it does not matter. It's only a test)

Location: Dallas Fort Worth, Texas

For 1st of July, 12am (noon), with 0.2 albedo I got:

Eg = 0.027 kWh/m2

Epoa = 0.85 kWh/m2

Eg = 3.2% of Epoa

For the same location and time but with albedo 0.85:

Eg = 0.12 kWh/m2

Epoa = 0.95 kWh/m2

Eg = 12.63% of Epoa

So just by increase of albedo the Epoa has risen by 10%.

PVsyst albedo page, says that PV output can be raised by 5-10% in case of snow on the ground.

That's why I want to know more, about which value to chose for albedo in which cases (not talking about snow or water surface areas).

[george]

Thank you Marvin.

What would be the "large body of water"? Not a backyard swimming pool? But a river, lake, sea? Could you specific, which one of these?

Also when you say "next to a body of water...", what does "next to" approximately mean? A sea-side cottage up to 100 meters from the coastline?

Again I understand that there might not be a precise answer to all of this, but what about an approximate one?

[george]

Thank you Marvin,

"PV array seeing" a particular area around it is basically like if instead of PV array on a roof, there would be a window on the same place. What a person could see through that window, would be "PV array seeing"? Did I get that right?

[george]

Thank you Marvin,

I can see Hamon Engineering is in good hands.

[André Mermoud]

Your comparison with a window is correct for a vertical plane.

However the additional yield of the albedo goes with (1-cos(tilt)). If this is 100 % for a vertical plane, it is only (1 - cos(30)) = 13.4% for a 30° plane, and 6% for a 20° tilted plane.

[george]

Thank you André,

But I am not sure I have understood you.

You compared how lower tilt angles lower the albedo effect on POA ground reflected radiation.

But how is that related with "looking through" the window comparison of how solar panel "sees" different areas (with different albedos) around it?

[george]

Our analogy of looking out from the inside of the window is only good for showing you what area might be able to reflect light onto the window, it does not tell you how much sunlight will come through the window.

 

But that was not the problem. I understand that lower tilt angles (that is: lower roof angles) lower the albedo effect on POA ground reflected radiation.

The issue was to explain, what did you mean by "PV array seeing" in context of what area needs to be considered on reflecting the light onto the window, due to estimation of the average albedo. If I understood it correctly. this is what you meant (see attached photo for simplification).

So in case of tilt angle = 90 (upper sketch):

averageAlbedo = 1/4*0.25 + 1/4*0.75 + 2/4*0.20 = 0.40

While if tilt angle is 40 (bottom sketch):

averageAlbedo = 1/3*0.25 + 1/3*0.75 + 1/3*0.20 = 0.35

I apologize in advance for the quality of the sketch. My intention is not to banalize the discussion, just to check whether or not I understood the explanations.

[george]

Ok. I was not interested in question number 2. That one is clear.

Only in question 1.

So did I correctly understand the explanation of your answer to question 1 in the upper post?

(just to add that my reason for using 90 and 40 tilt angles was to explain the difference in what "PV array seeing" depending on the tilt angle. Not to show how these angles affect the POA ground reflected radiation).

[george]

Thank you Marvin.

[André Mermoud]

The albedo effect corresponds indeed to what you would see across a window.

However this would correspond to a vertical PV plane (façade).

The albedo contibution, as "seen" by the collectors, is proportionnal to (1 - Cos(tilt)). This means that:

- for a vertical plane (Tilt = 90°), the contribution is 100%.

- for an horizontal plane (Tilt = 0), the contribution is = 0.

- for a 30° plane, it is 1 - 0.866, i.e. about 13.4%.

- and for a 15° plane, it is reduced to 3.4%.

NB: if you have a row-like (shed) arrangement, only the first row "sees" the albedo. The shading factor on the albedo component will be (n-1)/n (n= nb of sheds).

[André Mermoud]

The albedo effect corresponds indeed to what you would see across a window.

However this would correspond to a vertical PV plane (façade).

The albedo contibution, as "seen" by the collectors, is proportionnal to (1 - Cos(tilt)). This means that:

- for a vertical plane (Tilt = 90°), the contribution is 100%.

- for an horizontal plane (Tilt = 0), the contribution is = 0.

- for a 30° plane, it is 1 - 0.866, i.e. about 13.4%.

- and for a 15° plane, it is reduced to 3.4%.

NB: if you have a row-like (shed) arrangement, only the first row "sees" the albedo. The shading factor on the albedo component will be (n-1)/n (n= nb of sheds).

[george]

Thank you for the reply André.

For some reason I have not been informed about this reply by email. I have just seen it now.

When you say:

The albedo contibution, as "seen" by the collectors, is proportionnal to (1 - Cos(tilt)).

 

by "albedo contribution", you mean: the contribution of albedo to POA ground reflected radiation?

Why is it only "(1-cos(tilt))"?

Why isn't it "(1-cos(tilt))/2" as given by Sandia formula:

 

Eg = ((GHI x albedo x (1-cos(tilt))/2)

 

?