Calculating energy payback time for Photovoltaics

[bernard]

The paper itself does not specifically deal with the definition of Energy pay back time and its factors. Instead on the very beginning of the paper, it points out a reader to these three sources:

- IEA, Photovoltaics Power Systems Programme - Methodology
Guidelines on Life Cycle Assessment of Photovoltaic Electricity. 2011.

- Raugei, M. Energy pay-back time: methodological caveats and future scenarios. Prog. Photovoltaics 2012, DOI: 10.1002/pip.1249.

- Fthenakis, V.; Kim, H. Photovoltaics: Life-cycle analyses. Solar Energy 2011,85, 1609−1628.

These further mention research for mono-crystalline silicon PV, and mono and poly crystalline silicon PV's in commercial and residential projects. Open rack and flush mounts. Some specific values for embodied energy of inverters, wirings, and flush mount profiles are given per square meter, which are somewhat similar to my project. So I will use those.

[J.P.M.]

Thank you for the advice J.P.M.

And everyone else too.

The solution to my initial question was found in foo1bar's reply (thanks foo1bar):

You're welcome.

So, if your solution is found in that paper, it looks to me like you are extrapolating observations/data about the global nature of PV and it's impact on past and future consumption of global resources and then applying those data to a residential PV system.

[bernard]

Thank you for the advice J.P.M.

And everyone else too.

The solution to my initial question was found in foo1bar's reply (thanks foo1bar):

http://pubs.acs.org/doi/full/10.1021/es3038824
"Energy Balance of the Global Photovoltaic (PV) Industry - Is the PV Industry a Net Electricity Producer?"
would be the paper to look at since this is for theoretical calculations.

[J.P.M.]

I am well aware of the "significant digits" but the scope of this inquiry was not that and I respectfully use the OP's numbers to illustrate my point of view. Maybe my point of view was incorrect and if so, I apologize. I will bow out of this conversation before it goes off topic......

If by target you mean the subject of the original post, I'm not sure it ever was on target to any appreciable degree.

[gregvet]

Looks to me like you are both trying to separate fly crap from pepper.

Bernard: respectfully, get some background on the basics of solar energy. Also, some information about the math and use of something called "significant digits" wouldn't hurt either one of you. Anything beyond about 2 decimal places in these respects is mostly meaningless.

I am well aware of the "significant digits" but the scope of this inquiry was not that and I respectfully use the OP's numbers to illustrate my point of view. Maybe my point of view was incorrect and if so, I apologize. I will bow out of this conversation before it goes off topic......

[J.P.M.]

Looks to me like you are both trying to separate fly crap from pepper.

Bernard: respectfully, get some background on the basics of solar energy. Also, some information about the math and use of something called "significant digits" wouldn't hurt either one of you. Anything beyond about 2 decimal places in these respects is mostly meaningless.

[bernard]

With all due respect gregvet, I think you are wrong.

You can not calculate the DCsystemSize by using overall area of your PV array.
It has to be the active area of your PV array.
Check the Solar cell efficiency wiki page, and the upper reply by pleppik:

"Solar cell efficiency is calculated by dividing a cell's power output (in watts) at its maximum power point (Pm) by the input light (E, in W/m2) and the surface area of the solar cell"

So it's the "area of the solar cell" = active area.

That is what I am trying to ask: Why did Solarworld's Sunmodule Plus SW 270 mono panel used the overall area(1.676675 m2) for calculation of their module efficiency whereas they should have used their active module area?

[gregvet]

Thank you for the reply gregvet.

Could you elaborate on why the upper formula is wrong:

activeArea = DCSystemSize(STC)/(1000W/m2 * moduleEfficiency/100)
activeArea = 270W/(1000W/m2 * (16.10%/100)) = 1.677m2

?

That's exactly the way, one could calculate an array's active area, when both DC system size and module efficiency, are known.

All you did was to calculate the active area which is the exact dimensions of the module using the theoretical irradiation and efficiency. Your result is an area with a given efficiency. My calculations of DCsystemSize were based on the theoretical irradiation with the given efficiency.

[bernard]

You have the math wrong. The surface area of the panel is 1.676675 m^2. If we use a theoretical number of solar irradiation at 1000W/M^2, then the theoretical total irradiation is 1.676675M^2*1000W/M^2 = 1676.675W for the given size panel. Since the module efficiency is 16.10%, then the effective maximum watts for that module is .1610*1676.675W = 269.94W which is about 270watts

Thank you for the reply gregvet.

Could you elaborate on why the upper formula is wrong:

activeArea = DCSystemSize(STC)/(1000W/m2 * moduleEfficiency/100)
activeArea = 270W/(1000W/m2 * (16.10%/100)) = 1.677m2

?

That's exactly the way, one could calculate an array's active area, when both DC system size and module efficiency, are known.

[gregvet]

Thank you pleppik,

I took a look at this Solarworld's Sunmodule Plus SW 270 mono panel model, and noticed something confusing:

Apparently Module efficiency is 16.10%. Maximum power Pmax = 270W.
If we try to calculate the active area (cell area) of the module:

activeArea = 270W/(1000W/m2 * (16.10%/100)) = 1.677m2

On the other side, the overall (with frame) dimensions of the module, are: 1675mm x 1001mm. So total area would be:

totalArea = 1675mm * 1001mm = 1.676675 m2

This means that their activeArea is equal to their totalArea.

Does this mean that they incorrectly calculated their Module efficiency, and that it's lower than 16.10% ?

You have the math wrong. The surface area of the panel is 1.676675 m^2. If we use a theoretical number of solar irradiation at 1000W/M^2, then the theoretical total irradiation is 1.676675M^2*1000W/M^2 = 1676.675W for the given size panel. The DC rating is 270 Watts so the efficiency is calculated as 270/1676.675(using your numbers) = 16.10%

[bernard]

Thank you pleppik,

I took a look at this Solarworld's Sunmodule Plus SW 270 mono panel model, and noticed something confusing:

Apparently Module efficiency is 16.10%. Maximum power Pmax = 270W.
If we try to calculate the active area (cell area) of the module:

activeArea = 270W/(1000W/m2 * (16.10%/100)) = 1.677m2

On the other side, the overall (with frame) dimensions of the module, are: 1675mm x 1001mm. So total area would be:

totalArea = 1675mm * 1001mm = 1.676675 m2

This means that their activeArea is equal to their totalArea.

Does this mean that they incorrectly calculated their Module efficiency, and that it's lower than 16.10% ?

[pleppik]

Thank you pleppik.
I understand this depends on a number of factors, from producer to type of the module, mount configuration... But is there some rule of thumb or assumption method to determine how much area should be added to the calculated "collection area"? +3,4,5 %?

I think you'd have to look at a specific panel layout. I could see where, for example, the footprint might be only a few percent larger than the collector area for a roof mount, or substantially larger if you have rows of ground-mounted panels which need to have space between them.

[bernard]

The reason I was going in this direction is that the sources you cited used figures for the energy required to manufacture a square meter of PV, and I suspect that's supposed to be just the area of the solar cells themselves and not the frame or other module parts. It's a small difference in area, but it's important to understand what the calculations are trying to do in order to understand whether you're using the right numbers.
....
But this is only the area of the solar cells themselves; the actual installed array may take up more space.

Thank you pleppik.
I understand this depends on a number of factors, from producer to type of the module, mount configuration... But is there some rule of thumb or assumption method to determine how much area should be added to the calculated "collection area"? +3,4,5 %?

[pleppik]

It's interesting that judging from pleppik's quote below, one would assume that collection area has nothing to do with the angle of incidence or tilt angle, but instead it's the leftover area when you subtract the module frames, and gaps between cells - what it's left is collection area.
Did I get that wrong?

By "collection area" in my original response I meant the surface area of solar cells, as opposed to frames, gaps between cells, and anything else which might be part of the finished module but not actually generate power. This has nothing to do with how the panel is mounted, just how it's constructed.

The reason I was going in this direction is that the sources you cited used figures for the energy required to manufacture a square meter of PV, and I suspect that's supposed to be just the area of the solar cells themselves and not the frame or other module parts. It's a small difference in area, but it's important to understand what the calculations are trying to do in order to understand whether you're using the right numbers.

In any event, the area of a solar panel is easy to calculate given the efficiency and nameplate watts. Standard conditions are 1,000 W/m^2, so watts = 1000 * efficiency * area (where area is measured in square meters). Or, area = watts / (1000 * efficiency).

So for 15% efficient solar panels, you would expect the area of a 4kw array to be 4000 / (1000 * .15) = 26.67 m^2. But this is only the area of the solar cells themselves; the actual installed array may take up more space.

[J.P.M.]

It looks to me that the OP is looking for something that is definitionally different than what most of the responses will lead to. Maybe I'm missing something, but the OP's knowledge base appears different than what I'm familiar with.