Calculate Array Voltage

voltageThe output of  a mono-crystalline or poly-crystalline solar module changes as the its internal solar cell temperature changes. As these modules heat their voltage will decrease. As these modules cool their voltage will increase. When you look at a solar modules datasheet the voltage parameters provided are at an industry standard referred to as STC, Standard Test Conditions. STC is defined as 25C, 1000W/m2 and 1m/s wind speed (the light spectrum is also defined but this is a topic for another post).  You might be wondering why a wind speed is defined, this has to do with how the solar cell is being cooled by the light wind and will effect the performance of the modules output wattage.


Vmodule = ([ (Tamb + Telev – Tstc) x b] +V)
Where
Vmodule = The voltage of the module at a specific temperature
Tamb = Ambient temperature in Celsius
Telev = Temperature adder due to the mounting method used to affix the solar module to the ground or roof in Celsius
Tstc = Reference Cell Temperature, 25C
b = Temperature coefficient of voltage, volts/Celsius, this describes how the voltage changes with temperature
V = The voltage rating of the module that you want to adjust, Voc or Vmp


Lets look closer at the inputs needed:

Telev is an adder used to account for how heat will be trapped in the solar module as a result of how it is mounted. For example if you have an array that is ground mounted of a pole structure there is good air flow around the module keeping them cool. If you have an array mounted on a roof there is less air flow so the modules will run hotter. As a basic guideline I use the following adders, 20C for ground mounted with good airflow, 25C for roof mounted or tall standoffs or tilted and 30C for the typical shingle roof installation with flashing.

b is a coefficient that the module manufacturer will provide that determines how the voltage will change as temperature changes. Pay attention, this is often a negative number and it must be written in volts/C. Typically you willl find ratings Voc and Vmp of a smodule but if only the Voc is available you can use this to adjust the Vmp.

Using this to find the maximum and minimum voltage of an array we need to make one small change to the folmula:


Varray = ([ (Tamb + Telev – Tstc) x b] +V) x (Nseries)
Where
Varray = The voltage of an array of modules at a specific temperature
Nseries = The number of solar modules wired in series.
Tamb = Ambient temperature in Celsius
Telev = Temperature adder due to the mounting method used to affix the solar module to the ground or roof in Celsius
Tstc = Reference Cell Temperature, 25C
b = Temperature coefficient of voltage, volts/Celsius, this describes how the voltage changes with temperature
V = The voltage rating of the module that you want to adjust, Voc or Vmp


Here is how to use the above formula as it relates to selecting a grid connected inverter or MPPT charge controller. The idea is to calculate the maximum and minimum parameters and if they are within the parameters of the equipment being selected then you selected the correct component.


Calculate Array Minimum MPPT Voltage

VarrayMPPTmin = Varray when Tamb = Tmax and V = Vmp
Where
Tmax = the maximum temperature at the project site, C
Vmp = the solar modules Vmp rating at STC


Calculate Array Maximum MPPT Voltage

VarrayMPPTmax = Varray when Tamb = Tmin, V = Vmp and Telev = 0
Where
Tmin = the minimum temperature at the project site, C
Vmp = the solar modules Vmp rating at STC
Telev = zero, you are looking for the extreme so assume the mounting temperature adder is not at play


Calculate Array Maximum Voltage

Varraymax = Varray when Tamb = Tmin, V = Voc and Telev = 0
Where
Tmin = the minimum temperature at the project site, C
Voc = the solar modules Voc rating at STC
Telev = zero, you are looking for the extreme so assume the mounting temperature adder is not at play


As a side note about current(I):

Calculate the array current with Iarray = Imodule x Nparallel