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Array Mismatch Losses

Definitions

First let's define a sub-module as the set of cells protected by one by-pass diode. There are usually 3 sub-modules in series in a PV module.

The PV Array is made of strings of PV modules (or more specifically sub-modules) in series. The PV array has one or several strings connected in parallel.

For constructing the array I/V curve we have to:

  • Combine all I/V curves of the modules (or sub-modules) by adding the voltages; the current is the same in the full string.
  • Combine the I/V curves of the array by adding the current of each string.

The mismatch loss is defined as the difference between the sum of all Pmpp of each independent sub-module, and the Pmpp of the resulting I/V characteristics of the array.

Mismatch causes

We can observe several causes of mismatch:

The parameters or performance of each module are different

  • The real modules are never quite identical. At the output of the factory, the modules are sorted according to the parameters measured by a flash-test. They are attributed to their power class. On request, you can get the flash-test results of each bought module. The power class limits are usually given as the Power tolerances of the PV module. Nowadays each power class is of the order of 1.5 to 2% (5W / 300 Wp), and is "positive sorted".
  • However remember that the flash-test apparatus used for this sorting are not perfect: their accuracy cannot be better than at least +/-3%. Therefore the possible real dispersion between modules may be much higher.
  • Moreover after some hours of exposition, some modules are subject to the L_ID loss_, which is not identical for each module, and may increase the dispersion. This is specially treated in a specific tool in PVsyst.
  • With long term ageing, all the modules don't degrade in the same way. This leads to an increase of the Mismatch loss along the years, which may be evaluated in the Ageing tool.
  • The soiling may be uneven, and causes another source of mismatch. This effect is supposed to be included in the Soiling Loss factor parameter.
  • The array has partial shadings: this is treated in the Module layout part of the software, associated to the Near shadings construction. The mismatch is a part of the Electrical shading Loss in the loss diagram.
  • With bi-facial systems, the rear side irradiance may be inhomogeneous, even from sub-module to sub-module (in the width of a shed). There is a parameter for that, but in the present time we don't have reliable data nor model for its evaluation.

The string voltages are different

  • The string wire length is different from string to string, especially with big systems (centralized inverters).
  • The temperature may be different from part to part of a big system (colder at the edges).
  • With big systems, the irradiance may be varying from part to part of a system in case of clouds passages.This is a transient effect, affecting usually some few seconds or minutes within the hour. PVsyst neglect this in the present time.
  • Strings in different orientations, connected to a same inverter, have different current, but similar voltages (except perhaps for temperature). The calculation (option Mixed orientation) shows that the resulting mismatch is usually completely negligible.

The mismatch between strings is related to the voltage differences, and involves a displacement on the I/V curves. This results in general in very low power losses.

Mismatch parameter in the simulation - Default values

The mismatch due to the dispersion of the modules characteristics is a constant loss factor, valid for the whole simulation. This factor is extremely difficult to evaluate.

PVsyst offers a tool for the evaluation of the Module Mismatch as function of the Modules characteristics dispersion. This indicates that the loss is very low (less than 0.5%) for dispersions below 2%, but increases very quickly with the dispersion value.

In the version 6, due to the diminution of the power tolerances, we adopted a default value of 1%. This factor is usually set to 2% in most PV simulation software. In our calculations, this may be justified by the flash-tests uncertainty. In the new version 7, we passed again to a default value of 2%.

Mismatch principles and calculation

There are several tools for the understanding and the evaluation of mismatch effects in PVsyst.

For the Module mismatch, a button Detailed computation in the "Detailed Losses", or Tools > Electrical behavior of PV arrays gives access to a tool, which shows how a set of random modules I/V characteristics will combine, and the resulting I/V curve of the array.

The new tool "String Mismatch" (in "Detailed Losses") provides a pedagogic description of the principles of different mismatch modes. This shows namely that the current mismatch (within a string) is very important, because the current in the whole string is governed by the current in the "weakest" string. While the voltage mismatch between strings has much lower effects.

This tool also allows to quantify the losses due to the string lengths or temperature differences in your system.

For the Shadings mismatch losses, the Modules layout tool gives an explicit behavior of the strings I/V curves composition for each hour of a given day.