In 2008, the National Electrical Code (NEC) added a second paragraph to 690.7(A) stating, “When open-circuit voltage temperature coefficients are supplied in the instructions for listed PV modules, they shall be used to calculate the maximum PV system voltage as required by 110.3(B) instead of using Table 690.7.” This addition was made because Table 690.7 is very conservative and the temperature coefficient will provide a more accurate voltage increase.

Listed below is the maximum voltage calculation with open-circuit voltage temperature coefficients. As daunting as it may seem it’s quite easy once you’ve done it a few times. Let’s take a look at how it works:

Inverter maximum input voltage with the temperature coefficient percentage of the VOC calculation:

(STC temp – low temp) x temp coefficient % VOC x VOC + VOC = VMax

Inverter max voltage / VMax = Maximum modules per series string

For example:

Record-low temperature: -10ºC

Temperature coefficient of (VOC): – (0.30) %/ºC

Module open circuit voltage (VOC): 39.4 V

Inverter maximum input voltage: 600V

The STC temperature is 25ºC. This temperature needs to be deducted from the array location’s record-low temperature of -10 degrees as follows:

25 – (-10) = 35º difference.

Multiply the 35º difference by the temperature coefficient of VOC (I’ve used the positive value for an easier calculation, though you get the same result) then multiply by the module’s VOC:

35 x 0.0030 = 0.105

0.105 x 39.4V = 4.137V

This is how many volts each module will increase due to record-low temperatures. Add the voltage increase to the Module VOC. Then divide the inverter maximum input voltage by that number. This will give you the maximum number of modules that can be wired in a series string per that inverter and specific location.

4.137 V + 39.4V = 43.537 VMax

600V / 43.537 = 13.7 (round down to a whole number)

The maximum number of modules in this series string is 13. A series string of 14 could potentially produce more than 600V during record-low temperatures.

Lastly, the quantity of modules wired in series multiplied by the VMax equals your maximum system voltage.

13 x 43.54 V = 566 Maximum System Voltage

Voilà, we’ve determined the max PV voltage for our example system and are able to ensure a proper system design without fear of over-voltage for the inverter.

### The Author

### Ronnie Raxter (guest author)

Design Application Engineer

Dennis Connolly02/06/2015 at 2:32 pm

Great concise explanation about calculating Max PV Voltage for string sizing. Also, thanks for helping me a while back with our 6kW Sunny Boy Inverter system at our farm. We currently have the largest PV array on the Southern Illinois Electric Cooperative grid and the only install back feeding more than we consume 10 of the 12 months of each year.

Now, help me connect a Sunny Island to this system with your next article!

khaldoun05/07/2016 at 1:41 am

thnx for ur declartion ..

but i have two quistions :

the first is:

most of inverters assign the range of mppt voltage between (250 to 450 Vdc).. so if i connect a series of modules which produces a 550 Vdc .. will this (550-450 = 100 Vdc) be lost ?

i see most of calculations depends on max voltage of inverter and ignors the mppt range .. shouldn’t i have to rely on mppt range? if answer is no .. so how can i benefit from this mppt range ? what is the goal of it !!

second quistion is .. how can i calculate the maximum number of strings in parallel !!

i mean ,, if i have a 5 kva inverter .. (its solar charger 3KW) .. how can i calculate the max pv arrays nomber !!

thnx

Justin Dyke05/10/2016 at 10:36 am

Hello-

Often our spec sheets list the ‘rated’ MPPT voltage range – this range is used for efficiency calculations. The ‘operating’ MPPT voltage is often much larger and is the range your design should fall within. For example, our new Sunny Boy 5.0-US has a rated MPPT range of 220-480 VDC, but an operating MPPT range of 100-550 VDC. This operating range is the DC voltage range you want MPP voltage to remain within no matter what the temperature is. Outside of the rated range, the device efficiency may be slightly lower, but the inverter will still track the maximum power point within the full operating range.

Finally, for residential inverters, you must always ensure that open circuit voltage never exceeds 600 VDC. This is a code (and warranty!) limit. Remember that no power is being made at open circuit voltage (current from array is 0 A), so this is a separate calculation than ensuring the array’s maximum power voltage is within the inverter’s MPPT voltage window.

For the maximum numbers of strings you can bring in parallel to the inverter, this depends on the current limits for the inverter, and this varies from device family to device family. Our design tool Sunny Design can calculate the maximum number of strings based on your design location, module type and the inverter you wish to use!

Best,

Justin

omale Robinson james08/20/2016 at 12:35 pm

What is the maximum voltage shock when someone get in contact with electricity

Justin Dyke08/23/2016 at 4:58 pm

Hi Omale –

Be careful when working with electricity! When voltage is present, a shock occurs if the voltage causes current to flow through your body. How much current will flow depends on the resistance your body presents to this flow. With two sweaty hands, even low voltage can produce a strong shock across your heart.

Best,

Justin

Jacob McAfee01/31/2017 at 4:43 pm

Just wanted to point something out if you don’t mind. I was searching for the max Voc formula to refresh my memory since it had been a while since I had to use it. So I stumbled upon this since it was first on google (nice!) and I’ve installed your products before. Which I must say are a very high quality string inverter. But I must ask while I’m here, did you guys discontinue the the 600vdc Combi disconnect switch?

Sorry. Now to my point. I was a bit confused at first but quickly realized that although you did get the correct answer in your example, the formula is actually incorrect. It should start with (low temp-STC Temp) instead of the other way around. If you hadn’t dropped the negative and actually followed through with the math on your formula correctly, then your voltage adjustment would have been a negative 4.137v and therefore resulting in a max Voc of 35.03v. That would make me think I could string 17 modules in series for this inverter. But in reality, 17 modules in series at -10 would actually be 740.18Vdc. I dont think the inverter would think that.

I just wanted to point that out to be corrected so someone new to PV doesn’t just write down the formula and later go to design strings incorrectly. The main take away for anyone reading this, is that your number should always go up when temperature goes down. And in most cases its in the ballpark of a 3v-5v increase of the module Voc.

One additional note for others out there. You can always skip the formula and look up table 690.7 which would give you a correction factor of 1.14 for -10C. So 39.4Voc x 1.14= 44.916Voc. This is easier but as you can see the number is a little higher because the NEC is a little more conservative but you are allowed to use the formula if the module manufacturer does indeed provide the temperate coefficient. The NEC answer still ends up with 13 in series, but with I have ran a comparison on modules with lower coefficients and the NEC is usually one module less and therefore your design may not be as efficient this way.

I apologize if I sounded like a ‘know it all’ but I am not. I know I still have a great deal to learn in life. I just really love what I do and I really love talking about it. Cheers.

Jessica02/06/2017 at 9:32 am

Thanks for your comments, Jacob. I spoke with one of our technical trainers, who’s shared the following info.

Yes, we discontinued the Combi-switch as the fusing inside was only in one pole of the paralleled conductors, and NEC requires fusing in both poles for use with inverters without transformers, which covers all of our current string inverter line. These generally have a “TL” designator in the name somewhere that denotes “transformerless,” but we have removed it from the name in our most recent products.

With regards to the formula, yes, it should be understood that the resulting Vmax will always be higher than spec sheet (STC conditions) Voc. That is why it is commented that the positive value was used in the example.

Be careful about using the correction factor from the NEC table. Code states that if temperature coefficients are supplied (on spec sheet), they “..shall be used..instead of using Table 690.7” – NEC 2011 690.7(A). That is not an “allowed” where you are allowed to choose – NEC is demanding (and so could your plan checker) the more accurate number if the manufacturer supplies the coefficients.

SMA’s design program Sunny Design has a database of thousands of modules with these temperature coefficients available, and once the install location minimum temperature is selected, the program will calculate maximum string voltage automatically, avoiding any confusion about signs.

We hope this is helpful feedback for you.

shaymaa04/23/2017 at 11:01 pm

Thanks for these information

But if i always do my calculations at max voltage 600 v

Why data sheet include other max voltage 1000v

And other 800 v fir mppt??

And for inverters that have two ports what does mean by current for each port as example

33A for port A and 11A for B

Mike06/07/2017 at 9:23 am

Hello Shaymaa, in the United States, residential PV installations are limited to 600 VDC maximum. However, commercial systems can use up to 1000VDC if the equipment allows it, and utility can utilize even higher, again if all the equipment can support the maximum voltage. Thus, module and inverter data sheets will show max system voltage supported for each device. Similarly, there is a current limit for hardware. For our inverters, there is a short-circuit current limit for each input and for the device as a whole. Exceeding this limit will void the device warranty. In addition, there is a maximum current that the inverter will draw from each input in operation. It is acceptable to have the array be capable of providing more than this (as long as the short circuit current limit is not exceeded) – the inverter will simply draw only this max amount. As a designer, you must verify that all equipment (modules, inverters, wires, balance of system components) all can handle the maximum voltage and current of the designed system.

omar10/01/2017 at 2:54 am

Hey

what about calculating the minimum value for Vmp ?, in high temperature conditions the string may not attain minimum input voltage for the inverter , Do we use the same coefficient we used for Voc?

thanks

Alejandro10/03/2017 at 9:05 am

For sizing and dimensioning of PV systems, we recommend using our free software sunnydesingweb.com. You can also watch our recorded webinar at this link http://goo.gl/6YVhT8

Aris03/06/2018 at 4:54 pm

Thanks for this explanation, I do have a question though. Standard Test Conditions specify the PV cell temperature to be 25 degC. Are you suggesting that the record low ambient temperature should be subtracted from the STC cell temperature of 25 degC? This doesn’t sound right, because if we take the case where ambient temperature is 25 degC, that would give 0 degC difference and hence no voltage drop or rise. However, in reality due to the PV cell self-heating while generating, when the ambient temperature is 25 degC, the cell temperature will surely be greater than 25 degC, hence resulting in a decrease of Voc.

Therefore, shouldn’t we subtracting the cell temperature at the current conditions from the STC cell temperature of 25 degC?

Thanks,

Aris

Mike03/07/2018 at 10:13 am

Hi Aris! You are correct the cells will heat up during production. However, the lowest temperature for the system usually occurs right at daybreak, when the system is waking up. At that point, no current is flowing yet, but voltage is máximum on the inverter DC terminals as the array is at Voc. Thus, no compensation for self heating is used when calculating máximum system voltage. Regards.

Habib04/05/2018 at 9:25 am

Hi Mr. Mike,

The ambient temperature in Aswan, Egypt, at 9:00 AM is 5 C. The open circuit voltage of the solar panel is 47.2, while the voltage temperature coefficient is -0.31% V/C. What is the maximum open circuit voltage considering the temperature effect?

Mike04/06/2018 at 9:58 am

Habib, the maximum V is calculated from the MINIMUM temperature that the modules will EVER be exposed to. Lets assume that is -5 C – the system designer must choose the correct number however. Based on my GUESS of -5 C, adjust the 47.2V (measured at 25 C) upward using the -0.31%/C coefficient. This calculation yields Vmax = 47.2 + (-0.0031*47.2)*(-5-25) or 47.2 + (-.146)*(-30) or 47.2 + 4.39 or Vmax = 51.6V. Do this same math using the ACTUAL minimum temperature for your site instead of -5 C and you will calculate the appropriate Vmax.

Habib04/10/2018 at 2:18 am

Clearly, you mean (the ACTUAL minimum temperature) ambient or cell temperature?

Alejandro04/10/2018 at 8:56 am

Habib, you should take into account either the historical lowest temperature (if you want to be more conservative), or the average lowest temperature in Aswan, and of course we are talking about ambient temperature. You should also keep in mind that lowest temperatures usually occur right before dawn when there is no sunlight. I hope this answers your question. Best Regards.

Rana Noman Maqbool05/17/2018 at 10:33 pm

Dear

some invertor has a datasheet with VAC instead of DC. how we can find Inverter maximum input voltage.

thank you

regards

Noman

Mike05/21/2018 at 2:29 pm

Hello Norman! You must get this information from the inverter manufacturer. It is very uncommon that the maximum input DC voltage is not listed on the data sheet or in the installation manual in addition to the allowable AC voltage ranges.

Attila06/13/2018 at 2:26 am

Dear All!

I have a question about the Voc calculation. According to the results from the equation in the article I get much lover Voc values than the results in the Sunny Design Web calculates!

Does Sunny Design Web use this formula too?

Thank you!

Attila

Mike06/18/2018 at 10:26 am

Hi Atilla! Yes, the formula is the same. Ensure that your calculations result in Voc increasing when temperature decreases, this is an easy error to make. Also ensure that the module you have selected in Sunny Design is showing the same value for voltage vs temp coefficient as the spec sheet you are looking at.

cephas matanda06/16/2018 at 10:48 pm

hello help me on this one I have a 3kva 48vdc inverter charger its written max pv array 145vdc . is it possible to connect 3 solar panels 325w with voc of 45.5v in series.the panels vop is 37v inverter’s operating voltage is 60-115 v

Mike06/18/2018 at 10:28 am

Cephas, You need to contact the manufacturer of this inverter to ensure that operation between 115V and 145V is acceptable, and what will occur in that voltage range. Also, you may need to find from the PV module manufacturer what the coefficient of temperature for voltage is so you can calculate how the array voltage will change based on the temperature range for your install location. Depending on this install location, it is possible that the array would get into that voltage range of 115-145V.