# Temperature Coefficients

Etebari
Posts:

**8**✭
Quite often manufacturers only place Isc, Voc and Pmp temperature coefficients in their specifications but fail to post Imp and Vmp coefficients. Is there a way to derive those values mathematically without contacting the manufacturer?

0

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## Comments

26,204adminAs far as I know--These are physical characteristics of the silicon material itself and not really related to the specific manufacturer. Here are some numbers I would use (from a large Kyocera panel):

The above numbers are in percent--So you just use the specific Vmp/Imp/etc. of the panel you are calculating the temperature factors for... Notice that even for identical panels except one is 315 watts vs 320 watts--The numbers are slightly different (-0.46 vs -0.45 for Pmax). Just guessing but these are probably identical panels just sorted for rated output.

-Bill

10,311✭✭✭✭basically you'd be guessing. can you tell us what pv you are trying to find out about as somebody here may already know? worst case is you'd need to contact the manufacturer and while you are in contact with them suggest to them to list more specs.

8✭I am finding that most are close like you suggest. I've noticed these values make a big difference when sizing wiring.

8✭The PV panels I'm concerned about are the Phono Solar PS230P-20/U.

26,204adminSometimes, certain values do not really matter too much... For example Imp/Isc -- Current is not affected too much by temperature--and in any case, most people use heavier copper cable than required to carry the solar panel current because they want to keep losses low (in the 1%-3% range). So--there is not too much reason to worry about "safety factors" for current capacity (check the numbers for fusing/breakers/conduit fill/insulation rating/etc... But, usually you will be using 2x or more thicker cable to keep solar power losses low).

And for parallel solar panel strings (three or more identical panel strings in parallel)--There is usually a Series Protection Fuse listed--which is somewhere around 1.56x Isc (typically). But a lot of vendors seem to leave that requirement off their data sheets. That value (also missing from the Phono Solar data sheets) should be a requirement for the designer / inspector for a system sign off (one or two parallel strings, fusing is not needed or useful--But numbers should still be there to confirm).

I have seen a few high voltage (Vmp~100 volts or so) thin film panels (Dupont?) that had Isc in the 1-2 amp range, but a series fuse of ~15 amps. For those panels you can probably put three or four panels in parallel without fusing.

The usual "killers" in a design is Vmp-hot and Voc-cold... Vmp hot depresses Vmp voltage and can stop a charger from full charging current or prevent a GT inverter from starting/running. Hi Voc-cold can damage switching electronics.

-Bill

1,973✭✭✭Why? Wire sizing is based on current, and the variance in current from a PV module due to changes in temperature is very small.

34adminThermal Characteristics Phono Solar PS230P-20/U

Operating temperature range -45 to 85 °C

Temperature coefficient Pmpp -0.51%/K

Temperature coefficient Voc -0.37%/K

Temperature coefficient Isc 0.03%/K

If the manufacturer does not provide all the coefficients it is best to design the system using Isc and Voc just to be safe.

50✭✭✭✭Pmax = -0.46 %/C

Vmp = -0.52 %/C

Imp = 0.0061 %/C

This data doesn't make much sense. Imp temp coefficient is virtually zero. Therefore the temp coeff of Pmax should equal Vmp.

26,204adminThank you CalBiker--I agree--Imp should be closer to ~0.061 %/C (I think that there is an extra zero after the decimal point).

I am going to correct/adjust my previous post.

-Bill

50✭✭✭✭That looks lots better. If we want to be exact,

given:

TC_Vmp = -0.52 %/C

TC_Pmax = -0.46 %/C

Then

TC_Imp = ((1 - TC_P) / (1 - TC_Vmp)) - 1

TC_Imp = 0.0603 %/C

Cal

26,204adminThank you Cal!

Cool-We have a new poster that can take over writing some of the equation based answers/estimates I give--They even have a better chance of being correct too. 8):roll:

-Bill

50✭✭✭✭Thanks Bill, but now looking at my equation, I see an error. Results are the same.

Should be:

TC_Imp = ((1 + TC_P) / (1 + TC_Vmp)) - 1

Cal

17,615✭✭Well

everybodymakes mistakes. That's why we keep an eye on each other. :roll:8✭Attachment not found.Attachment not found.

Looks like I'm getting close to the values I expected, thanks for the input. TC for Pmp, Voc and Isc are on the PV label. Somewhere I read that the value of TCPmp=TCVmp+TCImp. Can anyone verify this? There will be dual Xantrex Controllers in parallel. Still trying to make sense of all of this so I can speed up design of other systems for myself.

26,204adminTCPmp = TCVmp

*TCImpPower = Voltage * Current

-Bill

8✭Thanks, hit the wrong key.

1,973✭✭✭Let V = voltage and dV = change in voltage due to temperature, and use the same notation for current and power

(1) P = VI

(2) P + dP = (V + dV)(I + dI) = VI + VdI + IdV + dVdI

subtract (1) from (2)

dP = VdI + IdV + dVdI

50✭✭✭✭As strange as it may look, TC_P = TC_V + TC_I is CORRECT.

Look at it this way, if TC_V is -1 % and TC_I is 1 % then the P changes by zero percent.

TC_P = -1% + 1% = 0%

Cal

1,973✭✭✭Not exactly. If V = 20 and I = 10, then P = 200.

Using your coefficient numbers, if you raise the temp 10 degrees, V = (1.1)(20) and I = (0.9)(10)

P = (1.1)(20)(0.9)(10) = 198

50✭✭✭✭Yep, not exactly.

Exactly it's:

TC_P = TC_I + TC_V + TC_I * TC_V

1,973✭✭✭When I get a chance I will test that with a real world example and see if it makes sense.