# Cell temperature or back-of-module temperature

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In the PVsyst help, the formula for calculating thermal losses is given as:

U · (Tcell - Tamb) = Alpha · Ginc · (1 - Effic)

http://files.pvsyst.com/help/thermal_loss.htm

The word "Tcell" suggests that this is the temperature of the actual cells inside the PV module, which is generally different (up to about 3 degrees Celsius hotter) than back-of-module temperature.

But in the following post, Andre Mermoud seems to be using back-of-module / Array temperature interchangeably with cell temperature:

http://forum.pvsyst.com/viewtopic.php?t=37&p=37

Can you please clarify, in the formula above, what "Tcell" refers to? We want to extract Uv and Uc from measurements that a client of ours has made of Ginc and back-of-module temperature, and want to know whether we should do some modeling to obtain cell temperature from back-of-module temperature to apply in that formula?

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The required temperature (for the one-diode model) is indeed the Tcelll.

However this is highly dependent on how you are defining (measuring) this back temperature.

You will have a difference between TCell and Tback only if you have a heat flux.

If you just glue a temperature sensor to the back side, you will indeed have a heat flux towards the outside medium (convection, radiation). In this case the difference will not be "3°C", as many people think, but a difference which is proportional to the (Tcell - Tair) difference (i.e. the irradiance), according to the heat resistivity of the back side (may be different with a plastic or a glass back coverage).

If you cover your sensor with an insulation, you will limit (suppress) this heat flux, and you will effectively measure the cell temperature.

Now if you put too much insulation, you will modify the effective equilibrium temperature of the cell at this point.

At the University of Geneva, we did a comparison with a special module equipped with a thermocouple within the encapsulation, and several ways of measurement.

We found that the best compromise was to cover the sensor with a polystyrene piece of about 7 x 7 x 1 cm.

Please see the FAQ How is evaluated the module temperature during simulation ?

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Thanks André, that clarifies things!
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I forgot to ask: In the same formula "U · (Tcell - Tamb) = Alpha · Ginc · (1 - Effic) ", could you clarify how PVsyst calculates "Effic"? For example, is Effic is the STC efficiency? Or maybe one of the hourly output variables such as maybe EffArrR, or EffArrC, or other ?

We want to use measured back of module temperature, wind speed, ambient temperature and Ginc to derive Uc and Uv for one of our clients who has gathered these measurements, and want to make sure we correctly understand your equation so that we can fit the coefficients appropriately.

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In some applications outside of the simulation, this is a "standard" value (in the hidden parameters).

During the simulation, PVsyst estimates the efficiency of the module with an initial efficiency, and then uses it in this expression (one iteration).

By the way this value has a very low impact in the U evaluation: a difference of 1% (in efficiency) will give a difference of 1% on the U-value or the Temperature difference, i.e. 0.35°C if you have a DT of 35°C.

The U-value has a very high uncertainty (5 to 10% or more if not really measured).

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Thanks André.

You wrote "During the simulation, PVsyst estimates the efficiency of the module with an initial efficiency, and then uses it in this expression (one iteration)."

Can you specify how the estimation is done? Is the estimate equal to the STC module efficiency? If not, can you indicate how it is calculated (what equation, or reference to the method you are using)?

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This should represent the energy effectively removed from the PV modules (cell), i.e. the efficiency after irradiance and temperature losses.

Now as I previously said, little difference don't have any impact in the expression.

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• 4 months later...

André,

The information above was useful. I am also trying to determine system specific Uc and Uv coefficients from field data. My first step is to make sure that I can duplicate values calculated from a general weather file in PVsyst. I am trying to use the output parameters from PVsyst to calculate Tcell, and I am comparing this to the value calculated by PVsyst. I would like them to be identical, so that I'm sure I am using the correct parameters, but I cannot seem to get them to be identical.

I have verified that for my simulation:

Uc=20

Uv=0

Alpha=0.9

I am using the following PVsyst output parameters:

Tamb=T Amb

v=WindVel

Ginc=GlobEff (as opposed to GlobInc: per you comment in http://forum.pvsyst.com/viewtopic.php?f=25&t=2739&p=7224&hilit=irradiance+input+to+thermal#p7224)

For the efficiency, I have tried both EffArrC and EffArrR

Then I plug the above values into the following equations to calculate Tcell

Tcell = Tamb + 1 / U · ( Alpha · Ginc · (1 - Effic) )

U = Uc + Uv · v

Finally I compare this calculated value (for all hours in the weather file), and compare it to the following.

Tcell=TArray (per your comment in http://forum.pvsyst.com/viewtopic.php?f=25&t=3148&p=8046&hilit=cell+temp+in+output#p8046)

The differences between my calculated value, and the TArray value are about -0.3 to 0.1 if I use EffArrC, and about 0 to 0.35 if I use EffArrR. Based on your previous comment in this thread, I assume that the efficiency being used internally for this Tcell calculation is different from both of these outputted efficiencies. Is that likely why my values are not matching? is there any way I can use the same efficiency value that PVsyst is using internally, so that I can calculate the same Tcell value? If I did, then I would have a robust method for using site data to come up with accurate Uc and Uv values for similar system types.

Another comparison I did, was to use all of the outputted parameters to calculate Effic from the thermal equation, and then I compared this to the two outputted values EffArrC and EffArrR - I did not get a 1:1 correlation for either.

Mike Anderson

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The only way of estimating the Uc and Uv values corresponding to your site is to avail of on-site measured data (Tcell, Tamb, Gincid and Wind velocity). Theses measurements should be performed in hourly values (or sub-hourly), and cover a significant period, representing all meteo situations (ideally several months). The Uc and Uv values will then be derived from these data by a bi-linear fit.

Now what you are doing here is to use the PVsyst model (which involves the Uc value, and Uv=0) for trying to evaluate Uc and Uv values (that you are "supposing").

This doesnt make sense: It's the snake biting its tail.

The only thing you are doing here is to check the calculation of PVsyst. And of course, if you don't use the exact calculation mode (variables) used by PVsyst, you will have different results.

NB: The Uv = 20 W/m2K that you have chosen here corresponds to a semi-integrated system. Please carefully read the help "Project design > Array and system losses".

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Thanks André,

I think I may not have been clear enough in my question. I understand that I will need to use site information to determine system specific Uc and Uv values. Before I go to that step, I want to make sure I have the calculation done by PVsyst completely understood, so that I can use it correctly with my site data. To make sure I understand it correctly, and that I am using the correct parameters, I tried performing a simple calculation, but it is not matching the PVsyst output correctly. Can you please consider the following:

I am using model input parameters and PVsyst calculated output parameters, as specified below:

• Uc=20 (model parameter used in simulation)

Uv=0 (model parameter used in simulation)

Alpha=0.9 (model parameter used in simulation)

Tamb=T Amb (from the simulation output)

v=WindVel (from the simulation output)

Ginc=GlobEff (from the simulation output)

Effic=EffArrC (or EffArrR) (from the simulation output - I tried both of these)

I then put these values into the equations below, and calculate Tcell:

• Tcell = Tamb + 1 / U · ( Alpha · Ginc · (1 - Effic) )

U = Uc + Uv · v

I would expect the Tcell calculated from above to equal the value outputted by PVsyst:

• Tcell=TArray (from the simulation output)

but it does not.

I suspect that this is because the Effic used in the internal PVsyst calculations is not equal to either EffArrC or EffArrR. If this is true, then I'm wondering if there is a way for me to know, or calculate the same Effic used by PVsyst in the Tcell calculation, so that I can duplicate it.

Once I am able to duplicate the Tcell calculation done by PVsyst, then I will move forward with the next phase of my work, and use site information, along with measured Tcell, to determine site specific Uc and Uv values.

Thanks for working through this with me.

-Mike

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• 2 weeks later...

For the temperature evaluation at eac hour, PVsyst doesn't use EffArrC nor EffArrR, which are yearly averages, and for the whole system.

It calculated a first evaluation of the Tarray with the STC efficiency.

Then it recalculates the PV module output at Geff and evaluates the real efficiency at this temperature.

Finally it will use this efficiency in the temperature evaluation (i.e: one iteration).

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Thanks, two follow on questions then:

1) After the steps you just specified, I assume this final Tcell is used in another (final) module performance calculation, correct?

2) Is there an output for "real efficiency"? I believe there is not. If not, then I assume I could determine it at each timestep by using the Tcell and U equations, with all of the other config and output values (mentioned previously in this post), couldn't I.

-Mike

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• 5 years later...
Posted (edited)

Thanks for the above dialogue. Thus, it seems to me like it would be more clear and consistent if each usage of "Tmod" in the PVsyst Help Menu (I count approx. 5 instances) changes to "Tcell". Also, if the output of PVsyst is Tcell (not TArray). Or, if it stays TArray, it could be more clear that TArray is "Average CELL temperature during running" (not MODULE). This is because module temperature, implying PV module backsheet surface temperature during operation, is not the same as cell temperature. There's also the option to export columns of both Tcell and Tmod, where the difference is attributed to the temperature delta (gradient) from backsheet surface to PV cell according to the King/Sandia equation & corresponding coefficients in , where PV cell operating temperature Tcell is higher in temperature (i.e., runs hotter) than PV module backsheet surface temperature during operation Tmod. One more note: The same PVsyst thermal model equation appears twice in the help menu in different forms: One using Tmod and one using Tcell. By and large in the PV industry (e.g., in literature on PV performance such as ), these are two different physical variables representing two different physical measurands.

 King, D. et al, 2004, “Sandia Photovoltaic Array Performance Model”, SAND Report 3535, Sandia National Laboratories, Albuquerque, NM.

Edited by kjs55
Change order of word "operating"; add word "in"