Calculating energy payback time for Photovoltaics

[bernard]

The collection area (perpendicular projected area of incoming sunlight on the panels) is an easy geometric calculation as long as you know the angle between the perpendicular to the panel surface and the incoming sunlight angle.
This will vary over the course of a day and will vary with time of year, and that calculation is automatically done by PVWatts and other array design tools. But that result is also combined with climate and altitude effects, so it is hard to separate out.

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?

4. Finally, you should check whether the area used for the energy calculation is #3 is the total module footprint, or only the collection area. In other words, do you count the module frame, any gaps between cells, etc. This non-active area might be significant (especially if these are smaller modules with more frame per collection area).

[inetdog]

4. I only took the 35m2 for 4kW. I guess that's the overall area, not sure.
Do you know of any methods to calculate this collection area out of the overall area?

The collection area (perpendicular projected area of incoming sunlight on the panels) is an easy geometric calculation as long as you know the angle between the perpendicular to the panel surface and the incoming sunlight angle.
This will vary over the course of a day and will vary with time of year, and that calculation is automatically done by PVWatts and other array design tools. But that result is also combined with climate and altitude effects, so it is hard to separate out.

[bernard]

Thank you for the reply pleppik,

1. PVWatts v1 mentions that 4kW PV array corresponds to 35m2 (377ft2)
How did you calculate the 35m2 area, according to the nameplate DC power rating(4kW) and module efficiency (11%)?
By calculating the maximal efficiency?
ni_max = (4kW/(1kW/m2 * 35m2))*100
area = 4kW/(1kW/m2 * (11%/100))

I always thought that when one talks about the PV efficiency of mono/poly crystalline silicone, some thin-film PV, or any other type of PV, it's not related with maximal efficiency, but rather some average efficiency?
Is this a rule that a maximal one is always taken?

2. It's estimated by PVWatts. It's 3624 kWh per year actually, but I said 3000 kWh to make the number more convenient.
For 4kW array, Azimuth angle: 180, Titl angle: 51.15 (location's latitude), system losses: 14%.

3. The mentioned paper from the first post says recommends 2737 MJ/m2 for polycrystalline silicon PV modules. 1210 MJ/m2 is for thin-film. Paper is based on Japanese research from 2011.

The number I took (4070 MJ/m2) is from 2011, but from English research.
It recommends polycrystalline silicon embodied energy range from 1945 to 5660 MJ/m2, but then value of 4070 MJ/m2 as the one that needs to be taken (not sure why, really).

4. Do you know of any methods to calculate this collection area out of the overall area?

[pleppik]

I took a look at a number of sources related with energy payback time (EPT or EPBT) for PV systems.
Here is one of them, which suits the best to my needs:

EPT [in years] = Total primary energy use of the PV throughout its life cycle [kWh] / Annual power generation [kWh/year]

My polycrystalline silicon 4kw PV system, and outputs some 3000 kWh per year in London, United Kingdom.
I made some research and looks like when it comes to polycrystalline silicon panels, it takes around 4070 MJ/m2 (MegaJoules/ square meter) of embodied energy (on average. The span is 1945 to 5660 MJ/m2) necessary for an entire product life-cycle.
An area of my 4kW PV system is 35 square meters, so it takes:
4070 MJ/m2 * 35m2 = 142450 MJ = 142.45 GJ of embodied energy for entire area of the PV system.

When I convert this to kWh: 1GJ = 277.77 kWh = > 142.45 x 277.77 = 39568.3365 kWh.
This is basically the Total primary energy use of the PV throughout its life cycle.

So then EPT would be:
39568.3365 kWh / 3000 kWh = 13.19 years.

This is way too much, and I read some sources where it says that energy payback time for polycrystalline silicon PV systems is 2-3 years.

Where did I go wrong in my calculations?
Thank you for the reply.

I can think of a few figures you can double-check:

1. The 35m^2 you used for the area of the array implies around 11% efficiency, which is low by today's standards. A 15% efficient module would cover about 27 m^2 for 4kw. How did you get this area?
2. 3,000 kWh production for a 4 kw array is also low, but I gather London is not the sunniest place. Is this observed or estimated production?
3. The paper you link to has a table showing a range of 1.2GJ/m^2 to 4.0GJ/m^2 for the energy to produce solar cells, so the number you used looks too high, possibly by a factor of 3-4. Also, it is my understanding that solar cell manufacturing has been getting significantly more energy efficient over the past decade, so if you used old data the numbers will be too high.
4. Finally, you should check whether the area used for the energy calculation is #3 is the total module footprint, or only the collection area. In other words, do you count the module frame, any gaps between cells, etc. This non-active area might be significant (especially if these are smaller modules with more frame per collection area).

So while the math looks OK, you may want to check your assumptions. If you're off by a factor of 1.5-2.5 in a few different places, you can easily get results which are wrong by a factor of 10.

[foo1bar]

Hi gregvet,

No, not really. I respect your effort and time, maybe someone else will profit from from your reply.
I need this for theoretical calculations, as I do not know the purchasing system costs nor any additional costs, commissioning...

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.

And the answer I think you're looking for is that it takes 1-4 years of the panel making energy for it to produce the amount of energy that was used to manufacture it.
But for those of us in the real world we don't care about that - we care about actual economic payback. (which is often 4-8 years, but varies greatly depending on the costs of installing.)

[bernard]

Thank you gregvet,

The insolation value is not a problem.
PVWatts does not calculate energy payback time, nor does wunderground.com.

Thank you once again for your replies.

[gregvet]

Try googling PVWatts and start fronm there. You might find your answer or at least a start to where you can find the answer. You might also want to visit this site: http://www.wunderground.com/calculators/solar.html to get an insolation value for your specific site.

[bernard]

Hi gregvet,

No, not really. I respect your effort and time, maybe someone else will profit from from your reply.
I need this for theoretical calculations, as I do not know the purchasing system costs nor any additional costs, commissioning...

So it does not have to be 3000 kWh per year, it can be anything theoretical. Or some rule of a thumb value:

For example London receives 3 kWh/m2 per day (peak sun hours) which means it receives 3 hours of sun per day at 1 kW/m2. Lets say that the size of the PV array is 4kW and I pretend that its efficiency factor is 0.72. Then by using this rule of the thumb method, I can get the annual electricity output:

4kW array * 0.72 = 2.88 kW
2.88 kW * 3 sun-hours/day = 8.64 kWh/day
8.64 kWh/day * 365 days = 3153 kWh per year

So everything remains the same: I only know the size of my PV array: 4kW, its area: 35 m2, its annual electricity ouput: 3153 kWh (or 3000 kWh like in first post), and I know that its embodied energy is 142.45 GJ = 9568.3365 kWh.

Can this be used to calculate Energy payback time (EPT)?

In above example, I am getting too high value (13.19 years). Is that approach correct?

Thank you.

[gregvet]

EPT [in years] = Total primary energy use of the PV throughout its life cycle [kWh] / Annual power generation [kWh/year]

My polycrystalline silicon 4kw PV system, and outputs some 3000 kWh per year in London, United Kingdom.

Where did I go wrong in my calculations?
Thank you for the reply.

If you already know what your PV generates yearly, and you have the costs associated with purchasing the system, including any additional costs (new inverters, repairs out of warranty) and you know the rate structure of your POCO and the commissioning date, then you can calculate ROI. These are real numbers. I am not sure if you can truly calculate a energy payback time using partly theoretical and partly real numbers. Anyway, I did do a calculation and I came up with about 14 years based on the costs saved for electricity for my system as my POCO has a net-metering agreement with me and electric rate is 0.12/kWh.
After algebraic manipulations the formula that worked for me is: (A*B/(A-C))-B Where A = Initial cost of system. B = elapsed years since commissioning date((current date-commission date)/365.25), C = cost of electricity saved since start of system (Initial cost-remaining cost or kWh generated to date *(cost/kWh)). All numbers are real-not theoretical. I set up my ROI to calculate daily on an excel spread sheet since I can update my daily kWh usage/generation and the elapsed years and costs are automatically calculated. Don't know if that will help you.

[bernard]

I took a look at a number of sources related with energy payback time (EPT or EPBT) for PV systems.
Here is one of them, which suits the best to my needs:

EPT [in years] = Total primary energy use of the PV throughout its life cycle [kWh] / Annual power generation [kWh/year]

My polycrystalline silicon 4kw PV system, and outputs some 3000 kWh per year in London, United Kingdom.
I made some research and looks like when it comes to polycrystalline silicon panels, it takes around 4070 MJ/m2 (MegaJoules/ square meter) of embodied energy (on average. The span is 1945 to 5660 MJ/m2) necessary for an entire product life-cycle.
An area of my 4kW PV system is 35 square meters, so it takes:
4070 MJ/m2 * 35m2 = 142450 MJ = 142.45 GJ of embodied energy for entire area of the PV system.

When I convert this to kWh: 1GJ = 277.77 kWh = > 142.45 x 277.77 = 39568.3365 kWh.
This is basically the Total primary energy use of the PV throughout its life cycle.

So then EPT would be:
39568.3365 kWh / 3000 kWh = 13.19 years.

This is way too much, and I read some sources where it says that energy payback time for polycrystalline silicon PV systems is 2-3 years.

Where did I go wrong in my calculations?
Thank you for the reply.