To calculate solar panels needed in series and parallel?

[zohaib]

Hello,

I have started working on solar systems. I want some help in solar system designing. If i want to design 30KW On grid system. For this system if we have 250.W polycrystalline panels available with 31 KW inverter and specs are shown below. I want to know how we calculate no of solar panels strings needed for this system with no of panels needed in series. How we calculate this. Please guide and help me in this regard. Minimum and maximum no of solar panels connected in series and no of string possible.

	DC 600V
	DC 350V
	DC 250V~550V
	31.5kW
	AC 380V (±10%)
	50 / 60Hz (±5%)

[inetdog]

Saying 250W panels is not enough. We need the Vmp and Voc values too. And will there be very cold temperatures?

[zohaib]

Thanks for the response. Below are the Vmp and Voc values of the panel.

Vmp= 30.7
Voc=37.5

[jflorey2]

Hello,

I have started working on solar systems. I want some help in solar system designing. If i want to design 30KW On grid system. For this system if we have 250.W polycrystalline panels available with 31 KW inverter and specs are shown below. I want to know how we calculate no of solar panels strings needed for this system with no of panels needed in series. How we calculate this. Please guide and help me in this regard. Minimum and maximum no of solar panels connected in series and no of string possible.

This is basic math. Steps:

Determine max voltage allowed at the inverter input.
Determine max voltage per panel. This will be Voc multiplied by: 1-(temperature coefficient)*(25C-minimum temp in your area)
Figure out how many panels you can put in series by adding max voltages. For example:Max Voc 39 volts, max system voltage 600 volts -> 15 panels (585 volts)
Sometimes you'll want to keep the voltage within the MPPT range of the inverter, but that's rare - usually the operating voltage is significantly lower than the startup voltage limit so you're automatically within MPPT range.

Keep adding strings until you reach your power target.

If you want to figure out the _minimum_ string you can use, generally you want to calculate the minimum voltage of each panel. To get that, use Vmp then reduce it by calculating the MAXIMUM temperature by taking Vmp then multiplying by 1-(temperature coefficient)*(25C-maximum PANEL temp, which is significantly above ambient) Then make sure the resulting min panel voltage * number of panels is still within the MPPT range of the inverter. This is NOT the same as minimum input voltage.

And again, keep adding strings until you reach your power target.

[zohaib]

Thanks for the details. I have some confusion in calculating these values. I am sharing the panels specs kindly can you explain in more detail how we to calculate these values..
And which values we have to tale from panels specs sheet to use above formula.
Wait for your kind response.

[jflorey2]

Thanks for the details. I have some confusion in calculating these values. I am sharing the panels specs kindly can you explain in more detail how we to calculate these values..

OK. To calculate max voltage for each string:

It looks like they use 46C instead of 25C for nominal. So that means that you use a different offset. Let's assume that your minimum temperature wherever you are is -20C. So that means (46C - -20C) is 66C * -.35% (temp coefficient) which is .27. So you have to increase your voltage by 27%. So your worst case open circuit voltage will be 1.27x greater than the declared open circuit voltage. That means each panel can be as high as 47.5 volts. This is the max voltage per panel.

Now look at your inverter's specs. I will go with an SMA SB 5.0-US, a newer inverter from SMA. Max DC voltage is 600 volts. So that means that 12 panels will be 570 volts, which is OK. 13 panels will be 618 volts which is too much. So your max number of panels per string is 12.

Next let's do minimum string length. This inverter's rated MPPT range is 220-480 volts so you want to stay above 220 volts. Let's assume your max panel temperature is 70C, which would be possible for an installation in a hot area. So now we look at Vmpp. (46C-70C) = 24C * -.35%, so your voltage will go down by about 8%. Vmpp is 30.7 so final voltage is 28.1 per panel. This is the minimum voltage per panel. So 8 panels is enough (224 volts) but 7 panels is not (197 volts.)

So now we know that you can use strings that are between 8 and 12 panels long. We know you need 120 panels to get 30kW (DC) so you would likely do 10 strings of 12 panels.

[zohaib]

Thank you so much for your detailed explanation. So from your above calculations we can put maximum 12 panels in series and 10 strings in parallel. Few things i want to clear.
We have to use Nominal Operating Cell Temperature of panels (46C in this case) in doing these calculation. In the calculation 66C * -.35% (temp coefficient) it becomes 23 percent. Please conform this calculation. Then we have to add 1 in this is it right?
As you have said if inverter range is 220-480V then we have to stay above 220 volts. What about maximum strings we can have in this case?
Please tell me how we know about maximum panel temperature how we calculate this thing.
Wait for your kind response again.

[zohaib]

Hello,

I have one more question it will be very kind if you can help me in this regard.
This is about general solar system from 1 to 5 KW (residential systems) battery backup calculations.

Regarding battery backup if we want 5 hours, 8 hours and 10 hours backup for 1 to 5 KW systems. Then how we calculate this thing. Kindly tell me method how we do these calculation and which can also be used for bigger systems.

[jflorey2]

Regarding battery backup if we want 5 hours, 8 hours and 10 hours backup for 1 to 5 KW systems. Then how we calculate this thing. Kindly tell me method how we do these calculation and which can also be used for bigger systems.

First measure your loads. That's your ACTUAL loads. Not an estimate, not a "well, the refrigerator says 4 amps on its nameplate so we'll assume 480 watts." Measure your ACTUAL loads per day in kilowatt-hours. Then divide by 24. That is your hourly average load.

Next multiply this by the number of hours you want to run. Next multiply this number by a factor between 2 and 10. 2 if this is going to be a once a year sort of thing, 10 if you lose power every day for unpredictable amounts of time.

Next take that number and multiply by 1/efficiency of your inverter. So if your inverter is 90% efficient, multiply by 1.11. Next take that number and multiply by a factor representing your loss of battery capacity due to your discharge rate. (For large battery packs compared to load it would be around 1; for small packs it could be 1.5.)

That will give you the battery size you need.

[zohaib]

Please tell me also about my question above regarding Panels parallel and series connection.

[zohaib]

Thanks for your response again. You have mentioned factor between 2 and 10 please tell me how we take this number in our calculation(Its not clear). Let say our Total watt hours requirement is 19 kw hour per day. I am sharing example below it will be very kind if can explain this with this example. Please correct me if i am wrong somewhere.

Appliances	Watts	Quantity	Total Watts	Hrs/day run	Total Watt- Hrs
Fan Ceiling	100	6	600	9	5400
Energy savers	30	18	540	6	3240
Laptops	60	7	420	9	3780
Printer	500	1	500	1 (Hr max)	500
Refrigerator	500	1	500	12(With Full load)	6000
Total	1190	33	2560	37	18920

Power Consumption:
Total Watts=2600 W.
Total Watt-Hrs= 19 KWHRS per day= 19 units per day
Multiply loss factor = 19000 x 1.3 = 24700 Watt-Hours per day
Lets sayTotal peak hours = 5
Total watts generated = 24700/5 = 4940 W

If we use 250 W solar panels = 4940/250 = 19 Panels required.
Inverter size:

TOTAL WATT- of all appliances = 2600 W
Total Load watts = 2600 x1.3 = 3380 Watts

Now how we calculate battery backup of 5 and 8 hours. Wait for your kind response.

[jflorey2]

Thanks for your response again. You have mentioned factor between 2 and 10 please tell me how we take this number in our calculation(Its not clear).

That comes from a few places.
First, you should never discharge a lead acid battery below 50%. That means if you are going to need 120 watt-hours (12 volts at 10 amp hours) then your minimum battery size should be 20 amp hours, so worst case you discharge to 50%.

Second, your situation may require longer run times occasionally - say, when a blackout lasts longer than expected. Designing for 3 days of autonomy is common in off-grid systems, so perhaps planning for 3x worst case blackout would be prudent. In that case, you'd need (2x3)=6 times larger battery than you would expect from doing your calculations.

From your numbers, your minimum requirement is 24.7kwhrs of battery per day. If you assume 8 hours during the highest use part of the day that will represent about 75% of your use, so that's about 18.5kwhrs. Double that to prevent discharge below 50% and you are now at 37 kilowatt-hours of required storage.

The first thing this tells me is that you are going to want to be at 48 volts (lots of storage, peak loads of 2.5kW.) So you will need at least 770 amp-hours of storage. A Rolls-Surette S-1450 is good for 1124 amp hours. Discharging at a 16 hour rate you'd be down to about 1050 amp-hours, so that works. Cost $8400, total weight about 3000 pounds. You will also need an inverter/charger to maintain the battery pack; it must be capable of at least a C/15 charge, so that means a 3600 watt charger at absolute minimum. If you lose power every day that number has to go up, because you want to reach full charge regularly.

[zohaib]

Thanks for you help again. Actually i am new in this area and learning these things. Kindly if you can explain steps in more details then it will be very helpful for me to understand. Actually i want to know if we know our per day usage, inverter and panels known as i have shared in an example so how we calculate battery backup (batteries required). Lets say we have 200 AH,12V batteries with 50% discharge rate and we want backup time of 8 hours in a day. Then how we calculate this thing.
Another thing is if we have 1kw to 3w hybrid solar systems and we want 5 hours backup with these system then how we calculate this things that how many batteries we needed in each case.

Secondly i am waiting for your response regarding this also.

Your Answer:

It looks like they use 46C instead of 25C for nominal. So that means that you use a different offset. Let's assume that your minimum temperature wherever you are is -20C. So that means (46C - -20C) is 66C * -.35% (temp coefficient) which is .27. So you have to increase your voltage by 27%. So your worst case open circuit voltage will be 1.27x greater than the declared open circuit voltage. That means each panel can be as high as 47.5 volts. This is the max voltage per panel.

Now look at your inverter's specs. I will go with an SMA SB 5.0-US, a newer inverter from SMA. Max DC voltage is 600 volts. So that means that 12 panels will be 570 volts, which is OK. 13 panels will be 618 volts which is too much. So your max number of panels per string is 12.

Next let's do minimum string length. This inverter's rated MPPT range is 220-480 volts so you want to stay above 220 volts. Let's assume your max panel temperature is 70C, which would be possible for an installation in a hot area. So now we look at Vmpp. (46C-70C) = 24C * -.35%, so your voltage will go down by about 8%. Vmpp is 30.7 so final voltage is 28.1 per panel. This is the minimum voltage per panel. So 8 panels is enough (224 volts) but 7 panels is not (197 volts.)

So now we know that you can use strings that are between 8 and 12 panels long. We know you need 120 panels to get 30kW (DC) so you would likely do 10 strings of 12 panels.

My question:

So from your above calculations we can put maximum 12 panels in series and 10 strings in parallel. Few things i want to clear.
We have to use Nominal Operating Cell Temperature of panels (46C in this case) in doing these calculation. In the calculation 66C * -.35% (temp coefficient) it becomes 23 percent. Please conform this calculation. Then we have to add 1 in this is it right?
As you have said if inverter range is 220-480V then we have to stay above 220 volts. What about maximum strings we can have in this case?
Please tell me how we know about maximum panel temperature how we calculate this thing.
Wait for your kind response again.

[jflorey2]

Thanks for you help again. Actually i am new in this area and learning these things. Kindly if you can explain steps in more details then it will be very helpful for me to understand. Actually i want to know if we know our per day usage, inverter and panels known as i have shared in an example so how we calculate battery backup (batteries required). Lets say we have 200 AH,12V batteries with 50% discharge rate and we want backup time of 8 hours in a day. Then how we calculate this thing.

I thought I just did that . . .

Most people do not use an even amount of power all day; they use it in "spurts" depending on what they have in their house. If you have air conditioning, usage peaks around 4pm at the hottest part of the day. If you don't, usage peaks around 7pm when ovens, lights and TV's are in use. For most people, if you took the heaviest-use 8 hour segment, you'd see 75% of their load take place in that time.

So for you, 75% of your load is 18.5kwhrs. That's what your battery system would have to support. To make sure you never discharge below 50% you need 37kwhrs of battery. You want to use 12V 200AH batteries. These are a VERY BAD IDEA since you will end up with lots of parallel strings. But if you were so foolish as to try to use them, you would need 16 of them, in 4 strings of 4 to get 48 volts. Again, this is a VERY BAD IDEA.

Another thing is if we have 1kw to 3w hybrid solar systems and we want 5 hours backup with these system

OK. First off, your solar capacity doesn't matter. This is a backup-UPS type system, not a solar hybrid system. That means the power to recharge (and thus maintain) your batteries comes from the grid, not from your solar array. This is a good thing since you won't have to deal with matching your solar array to your battery bank.

At 5 hours you'd probably see a max of 50% of your usage during that time, so you'd be at 12.35kwhr storage. Double that and you are at 24.7. That's 11 batteries of the type you describe. You can't use 11 12-volt batteries in a 48 volt system so you would have to go up to 12 batteries.

So from your above calculations we can put maximum 12 panels in series and 10 strings in parallel. Few things i want to clear.
We have to use Nominal Operating Cell Temperature of panels (46C in this case) in doing these calculation. In the calculation 66C * -.35% (temp coefficient) it becomes 23 percent. Please conform this calculation. Then we have to add 1 in this is it right?

Your open circuit voltage at that temperature will be 23 percent higher. So to calculate the new voltage, multiply Voc by 1.23.

As you have said if inverter range is 220-480V then we have to stay above 220 volts. What about maximum strings we can have in this case?

If your inverter is designed to combine all the strings at the inverter, then the inverter will list the maximum # of strings AND the maximum current per string AND the maximum total current. (Sometimes it lists max total power instead; you can do the math to get the current.) If it is designed to use an external combiner box then it will list maximum current input. You must stay below that current.

Please tell me how we know about maximum panel temperature how we calculate this thing.
Wait for your kind response again.

A good rule of thumb is 35C above the maximum temperature you will see in your area. If the hottest temp you will ever see is 35C, then max panel temp would be 70C.

[zohaib]

Thanks for your help and guidance again. Really helpful.

[zohaib]

I have one more question. If i have to run 5 HP submersible pump having total lift of 40 ft. The water requirement is 3 cusec. Which capacity inverter and how many panels (250w) are suitable to run this pump and meet water requirement. I think 5 KW panels and 5.5 KW inverter works for this. Please guide me.
Wait for your response.