Relationship between efficiency and area required per kW

[shirleyzzz]

Hi All, I'm new to the forum and I have a question on the relationship between efficiency and area required per kW. I know when efficiency increases, the area required per kW reduces (proportionally?). So theoretically, multiplying efficiency and area required per kW would give a constant. But this is not the case, after I checked a few products on the market, even if they are the same type of PV panel.

For example, for monocrystallaine PV from Sunpower x-series, available at https://us.sunpower.com/sites/sunpow...lar-panels.pdf. There are two types of monocrystalline PV in this product sheet: SPR-X21-335-BLK and SPR-X21-345, with efficiency 21% and 21.5% respectively. The area required by each individual panel for these two types are the same (1558mm *1046 mm). The former has 335 W, while the latter has 345 W. But 345W divided by 335W does not equal to 21.5%/21%.

Is this expected, and why they are different? Could anyone help to explain the technical reasons behind? Thank you!

[J.P.M.]

Panel efficiency is measured indoors under a solar simulator that has radiative flux of approx. 1,000 W/m^2, and a light frequency distribution similar but not identical to actual solar irradiance.

The panels are held to a nominal 25 C. temp. for testing.

The MPP (max. power point) voltage for a panel is f(temp.). The MPP current is f( irradiance).

While there may be minor mfg. variations between panels on the theory of continuous process improvement over time, the actual differences between one panel's rating and the next may well be how individual panels do under test, with panels testing higher (> 345 W) rated and sold as 345's and those testing lower (< 345 W) rated and sold as 335 W panels. Note the spec sheet tolerances, note 12 at the bottom of the spec sheet and warranty doubletalk about output.

Both panels have the same MPP Voltage == 57.3 V.

The 345 Watt panel MPP current is 6.02 Amp. The 335 panel MPP current is 5.85 Amp.

Rated power = MPP Voltage X MPP current.

For the 345panel (57.3 V) x (6.02 A) = 344.9 W.

For the 335 panel (57.3 V) X (5.85 A) = 335.2 W

The irradiance for each panel based on gross dimensions = Area X irradiance flux = (1558 mm X 1046 mm)/10^6 X 1,000 W/m^2 = (1.645 m^2/panel) x 1,000 W/m^2 = 1,645 W/panel

Efficiency for the 345 panel based on gross dimensions = 344.9/1,645 = 20.97 %

Efficiency for the 335 panel based on gross = 335.2/1,645 = 20.38%.

The spec sheet stated efficiencies seem to use use something closer to net cell area excluding at least part of the frame and rounding the result.

[shirleyzzz]

I see. Thanks for your helpful explanation. Going back to my original question: whether the product of multiplying efficiency and area per kWp would be a constant. I found it is not by browsing the products online. Based on your explanation of how the Efficiency and Rated Power are calculated, I think I know why:

Rated Power = MPP Voltage * MPP Current
Efficiency = Rated Power /(Area1*Irradiance), here the Area1 is the area on which solar irradiance hits, in other words, excluding the frame.
Area per kWp = Area2/Rated Power, here the Area2 is the area including the frame.

Therefore, Efficiency * Area per kWp would be: Area1*Irradiance/Area2, although under the standard testing condition, the irradiance is the same, but Area1/Area2 is not always the same. Right?

[J.P.M.]

I see. Thanks for your helpful explanation. Going back to my original question: whether the product of multiplying efficiency and area per kWp would be a constant. I found it is not by browsing the products online. Based on your explanation of how the Efficiency and Rated Power are calculated, I think I know why:

Rated Power = MPP Voltage * MPP Current
Efficiency = Rated Power /(Area1*Irradiance), here the Area1 is the area on which solar irradiance hits, in other words, excluding the frame.
Area per kWp = Area2/Rated Power, here the Area2 is the area including the frame.

Therefore, Efficiency * Area per kWp would be: Area1*Irradiance/Area2, although under the standard testing condition, the irradiance is the same, but Area1/Area2 is not always the same. Right?

You're welcome. Hope it helps.

The "Area 1" and "Area 2" you are referring to are often defined differently for different mfg. and are somewhat arbitrary. If only the actual power producing areas of a panel were considered in the efficiency calculation, you'd have the cell efficiency. That's a different and higher number. It may or may not be a figure of merit.

Example: my older S.P. 327 spec sheet lists a "panel" efficiency of 20.1%, and a "cell efficiency of 22.5%, which would give a cell area 327.1/.225 = 1.454 m^2. That's pretty close to the area of the cells only as I measure it on my panels.

Bottom line: The area used to calculate panel efficiency is somewhat open to interpretation.

Another interesting point may be (or may not be , depending on your outlook), whether to include the open space between panels when figuring the "area efficiency" of an entire array.

I don't get too hung up on things like area efficiencies and instead spend more effort on things like most bang for the buck with respect to annual electricity production and it's monetary value with respect to what the array cost to purchase and what it costs to maintain.

If I may: What's the origin of your questions ?

[shirleyzzz]

Thanks for your interesting reply again. And you are absolutely right that the origin of my question is quite relevant to this discussion. What I'm trying to do are actually two analyses:
1) I know a specific area available for PV installation, and would like to estimate the potential range of installed capacity (in power), given current and future efficiency ranges.
2) I want to do some sensitivity analysis of how the change of panel efficiency will affect the levelised cost of each kWh of electricity production during the panel's lifetime.

I guess, based on our discussion so far, it means:

For 1) it is better to somehow figure out the "true area cover" (including framing and open space in between) it requires to install each kWp of panels. I should cover the worst and best practice among different panels, and consider the efficiency today and in the future.
For 2) I could keep the product of efficiency and area per kWp as a constant, meaning, the % of efficiency increase would be the same as the % of area per kWp decrease. In this case, I guess I have to pick a particular panel to start with.

What do you think?

[J.P.M.]

Thanks for your interesting reply again. And you are absolutely right that the origin of my question is quite relevant to this discussion. What I'm trying to do are actually two analyses:
1) I know a specific area available for PV installation, and would like to estimate the potential range of installed capacity (in power), given current and future efficiency ranges.
2) I want to do some sensitivity analysis of how the change of panel efficiency will affect the levelised cost of each kWh of electricity production during the panel's lifetime.

I guess, based on our discussion so far, it means:

For 1) it is better to somehow figure out the "true area cover" (including framing and open space in between) it requires to install each kWp of panels. I should cover the worst and best practice among different panels, and consider the efficiency today and in the future.
For 2) I could keep the product of efficiency and area per kWp as a constant, meaning, the % of efficiency increase would be the same as the % of area per kWp decrease. In this case, I guess I have to pick a particular panel to start with.

What do you think?

I don't believe I wrote or meant to imply the correctness (or what I may think incorrectness) of any of your writings. FWIW, since you ask what I'm thinking, and without rancor, I think you are on the right track but a bit naïve at this point. Consider there may be more to knowing the available area for an installation, how that available area is limited and how such considerations may affect the LCOE of an installation than you may be considering at this time.

How much experience to you have will solar PV design ? I respectfully suggest you may be putting the cart a bit before the horse at this point.

But, since you are asking, what else I think (or, to paraphrase a Yogi- ism, suspect)

First: If for a specific application and before anything else:
1.) Figure out the duty. For residential PV, this will mean analysis of the electric bill.
2.) Learn and understand the tariff/billing options available.
3.) Design the system for the lowest LCOE consistent with safety and needs.

If for academic purposes:
1.) Consider all factors that will reduce available area. This includes reductions for required fire setbacks and emergency access/egress.
It also includes long term considerations for reductions in available space for maintenance. For example, will access to panels in the middle of a 5 X 5 panel array be necessary ?
2.) Will shading impact available area ? A shading analysis may be required.
3.) Various mounting methods may have different packing densities. Example: My array's racking (mounting) has ~ 1" or so space between adjacent panels. The guy next door to me has ~ 0 space between adjacent panels.
4.) Will any proposed system LOCE or duty requirement benefit by tilting the panels ? If so, the latitude and local solar climate will play a factor in the row pitch (the distance between panel rows to minimize shading rows farther from the equator.

I'm not sure that what you seem to have in mind has a whole lot of practical application beyond how system cost as measured by some consistent criteria, be it first cost, LCOE or some other life cycle type method, is influenced by available area in a gross sense. Beyond that, there are probably some interesting areas to investigate dealing with the extra expense or tradeoffs of reducing the packing density of an array as may be required by legal or practical considerations.

Simply seeing how many solar panels can be crammed into an area while considering a various panel's area efficiency is a necessary first step, but it's only a first step. The devil and usable solutions are in the details.

Respectfully,

[foo1bar]

1) I know a specific area available for PV installation, and would like to estimate the potential range of installed capacity (in power), given current and future efficiency ranges.

For any real world case there will be considerations that will make the estimate incorrect.
For example:
1> fire protection setbacks
2> space needed for racking connectors
3> space for frames
4> "wasted" space because panels aren't exact multiple of the X or Y dimension


So for any real world scenario it will be done by "How many panels from vendor X can I fit in this space? From vendor Y? What's the wattage per panel range for Vendor X's design? What's the wattage range for Vendor Y's? What about Vendor Y's other line of panels that are 20% bigger in the Y direction?"

[shirleyzzz]

J.P.M. Both of my analyses are for academic purpose, and as you could probably tell, I don't have much experience with solar PV design and installations, and that is why I find it necessary to find someone like you in this forum to discuss. I guess the general meaning of your last reply is: I have simplified things. I also agree with you in this regard. Below are some thoughts I have corresponding to your suggestions for academic purposes.

1.) Consider all factors that will reduce available area. This includes reductions for required fire setbacks and emergency access/egress.
It also includes long term considerations for reductions in available space for maintenance. For example, will access to panels in the middle of a 5 X 5 panel array be necessary ?
3.) Various mounting methods may have different packing densities. Example: My array's racking (mounting) has ~ 1" or so space between adjacent panels. The guy next door to me has ~ 0 space between adjacent panels.
--->I will try to get a range from 0 to some kind of "maximum inter-panel space required", and consider it in my analysis.

2.) Will shading impact available area ? A shading analysis may be required.
--->This is out of my scope, and I clearly mention it in my study.

4.) Will any proposed system LOCE or duty requirement benefit by tilting the panels ? If so, the latitude and local solar climate will play a factor in the row pitch (the distance between panel rows to minimize shading rows farther from the equator.
--->Good point, I will try to get a range from 0 to a tilt angle given my local climate.

"I'm not sure that what you seem to have in mind has a whole lot of practical application beyond how system cost as measured by some consistent criteria, be it first cost, LCOE or some other life cycle type method, is influenced by available area in a gross sense." -->I didn't quite get what you mean here...

"Beyond that, there are probably some interesting areas to investigate dealing with the extra expense or tradeoffs of reducing the packing density of an array as may be required by legal or practical considerations."-->this is out of my scope.

foo1bar, I also realized thatthese practical considerations you mentioned, and that is why I'm trying to estimate a range of area per kWp given these considerations for my estimate.

[J.P.M.]

J.P.M. Both of my analyses are for academic purpose, and as you could probably tell, I don't have much experience with solar PV design and installations, and that is why I find it necessary to find someone like you in this forum to discuss. I guess the general meaning of your last reply is: I have simplified things. I also agree with you in this regard. Below are some thoughts I have corresponding to your suggestions for academic purposes.

1.) Consider all factors that will reduce available area. This includes reductions for required fire setbacks and emergency access/egress.
It also includes long term considerations for reductions in available space for maintenance. For example, will access to panels in the middle of a 5 X 5 panel array be necessary ?
3.) Various mounting methods may have different packing densities. Example: My array's racking (mounting) has ~ 1" or so space between adjacent panels. The guy next door to me has ~ 0 space between adjacent panels.
--->I will try to get a range from 0 to some kind of "maximum inter-panel space required", and consider it in my analysis.

2.) Will shading impact available area ? A shading analysis may be required.
--->This is out of my scope, and I clearly mention it in my study.

4.) Will any proposed system LOCE or duty requirement benefit by tilting the panels ? If so, the latitude and local solar climate will play a factor in the row pitch (the distance between panel rows to minimize shading rows farther from the equator.
--->Good point, I will try to get a range from 0 to a tilt angle given my local climate.

"I'm not sure that what you seem to have in mind has a whole lot of practical application beyond how system cost as measured by some consistent criteria, be it first cost, LCOE or some other life cycle type method, is influenced by available area in a gross sense." -->I didn't quite get what you mean here...

"Beyond that, there are probably some interesting areas to investigate dealing with the extra expense or tradeoffs of reducing the packing density of an array as may be required by legal or practical considerations."-->this is out of my scope.

foo1bar, I also realized thatthese practical considerations you mentioned, and that is why I'm trying to estimate a range of area per kWp given these considerations for my estimate.

Good luck in your academic endeavors.

If you're asking: What I meant with respect to practical application, if I understand what your looking for, is that what you seem to be looking for has already been pretty much beat to death, with ample literature and data available, copies of some of which are on my bookshelves. IMO, you're attempting to reinvent the wheel, but don't know much about the terrain you want to cover, or that others have already been there. Put another way, you don't know what you don't know and the answers are all around you.

Not to discourage you at all - quite the contrary, but as a practical endeavor, and meant as friendly and sincere, if perhaps blunt advice, I'd consider expending effort on the basics where you say you don't have much experience, and in so doing, as I suggested, keep the cart before the horse. Then, do a literature search.

Take what you want of the above. Scrap the rest.