How to define the "Mismatch Loss" parameter ?

[André Mermoud]

The mismatch parameter concerns the electrical differences between the modules in an array.

It reflects the fact that in a string of modules (or cells), the lowest current drives the current of the whole string.

The mismatch is computed by adding the I/V characteristics of each module, in voltage for each string, and then in current for each string in parallel. After that it recalculate the final Pmpp on the reswulting I/V curve.

Mismatch loss evaluation for modules characteristics dispersion

The discrepancies are mainly the dispersion of individual I/V characteristics, ideally as measured at at the output of the factory.

There is a tool for understanding, and statistically estimating the corresponding loss (button "Detailed calculation"), according to your effective distribution of "real" modules. This loss is a parameter that you have to fix in the simulation.

This mismatch effect evaluation is a stochastic process, which cannot be very accurate.

For crystalline modules, and a usual dispersion (RMS) of 2.5%, the tool (histogram on numerous calculations) will show an average loss of the order of 0.5%.

However things are not so simple, because:

- The modules may evolve (differently) after the installation (namely due to LID).

- Any flash-test manufacturer will tell you that with the best Laboratory instrument (class AAA) you cannot wait for an accuracy much better than 2%. Now instruments used in production at the output of the factory have probably a much higher uncertainty, of 3% or more...

With a RMS = 3% the mismatch loss will be of the order of 1%, and increases quickly with the RMS value.

Proposed default value

A recent study using results with "measured" optimizers on several dozens of PV systems seems to indicate that the real mismatch on the field is of the order of 2 to 2.5%.

Therefore with the version 7, we set again the mismatch loss default value to 2%.

In the version 5, this default was proposed as 2%, in accordance with most of the orther software.

In the version 6, PVsyst proposed a value of 1% (reduced due to the narrow tolerance in the modern PV modules deliveries).

But there is no "absolute value" of course. You can put here the value you can estimate according to your sample of modules.

NB: You can improve a little bit the mismatch loss by sorting the modules of comparable powers (or ISC) into the same strings. However this doesn't apply to the Flash-test uncertainty (which is a main contribution of the Manufacturer's initial data error), and is only valid at the commissioning time.

Mismatch between strings

The distribution of wire lengths for each string of a sub-array induces in a voltage distribution at the MPPT input. This is namely to be analyzed when consdering central vs string inverters.

However the I/V calculations show that the mismatch losses between strings of "reasonably" different voltages are very low. The discrepancies between these 2 options (central vs string) are of the order of 0.1 %.

See How is treated the gain of string inverters with respect to centralized ones?.

Mismatch and Ageing

The tool "Degradation" tries to take the discrepancies in long-term degradation characteristics between modules into account.

PVsyst proposes a mechanism (Monte-Carlo random process) for this evaluation. But sorry, the default values for the Mismatch evolution parameters are completely uncertain (only from my own "guess").

I don't know any study about the differential ageing between modules. The only available (and reliable) studies measure the real degradations of some very few modules, and find a degradation of around -0.3%/year as an average. I have chosen the default values for mismatch, in order to stay within the usual manufacturer's warranty after 20-25 years for a single module.

In the results, the ageing mismatch loss is part of the general "Mismatch" loss.

Mismatch due to partial shadings

The mismatch due to shadings is accounted in another part, i.e. the calculation of the electrical shading loss. You have an "accurate" estimation with the "Module Layout" tool, or a more generic and incertain with the "according to module strings" mode.

Now the electrical loss resulting from the I/V characteristics behavior under partial shadings is not only attributable to the electrical mismatch. There are two unrelated significant contribution:

- When a few cells are shaded in one sub-module, the other cells receive indeed some irradiance, which cannot be used and is completely lost.

- When a sub-module is shaded and the current is forced above its Isc value, the by-pass diode is activated. It consumes some energy (V diode * I string), provided by the rest of the array (therefore a loss).

These 2 kinds of losses are not recoverable in any way, even with power optimizers at the module (or sub-module) level.

Mix of different module samples

It is sometimes necessary to mix some modules of different power classes on a same inverter input.

This may be accounted for by defining an additional "Mismatch" loss contribution (to be added to the "normal" mismatch loss factor). However the effect of the mismatch between different strings (i.e. the voltage mismatch) is very low. Therefore you can simply perform the simulation with the higher module, and add a mismatch contribution corresponding to the weighted difference between the nominal powers.

As an example: if you have a sample of 30% modules of 250 Wp, and 70% of 255 Wp (i.e. 2% difference), you can perform the simulation with the 255 Wp, and define an additional mismatch of 2% * 30% = 0.6%.