The P50 - P90 evaluation is a probabilistic approach for the interpretation of the simulation results over several years.

This requires several additional parameters, which are not provided by the simulation process, and should be specified (assumed) by the user.

## Procedure summary

For activating the P50 - P90 tool, please open the button "Energy Management", page "P50 - P90 estimation" in the grid's project dialog.

This should be done after a first simulation, since by default the P50 value corresponds to the simulation output.

First choose the "Kind of Data", which will impact how the P50 value is determined.

Then determine the shift, weather data annual variability, and other simulation uncertainties.

Finally, you may specify whether you want P90 or other values. The result will appear on the report if the parameters are correctly specified (no warning).

NB: This feature is not available for Stand-alone and Pumping systems, where it is more difficult to define.

## Probability law

This approach supposes that over several years of operation, the distribution of the annual yields will follow a statistical law, which is assumed to be the Gaussian (or "normal") distribution.

P50/P90 represent different yield levels, for which the probability that the production of a particular year is over this value is 50%, resp. 90%.

The problem is now to establish the 2 parameters of this Gaussian distribution, i.e. the Mean value and the Standard deviation (named sigma or RMS).

The main contribution to those parameters will be the uncertainty and variability of the meteo data. But other uncertainties in the simulation process and parameters should be taken into account.

Uncertainties on Meteo data

Commonly available meteo (climatic) data have usually some uncertainties, of different kinds, which may produce very significant differences between sources, or years in a same source. These may be:

- The yearly variability, which is supposed to have a Gaussian distribution,

- The quality of the data recording, care of the operators, positioning, calibration and drift of the sensors, perturbations like shadings, dirt or snow on the sensors, etc.

- The presence of a not negligible horizon for terrestrial measurements,

- The location difference (distance of measuring station) for terrestrial measurements,

- The quality of the models used for interpreting the satellite data, which is in continuous improvement since 20 years,

- The evolution of the climate. In Europe, it seems that the irradiation has increased by as much as 5% since the beginning of the 21th century.

See the differences in the PVGIS data between the old database and the more recent "Climate-SAF" database.

Another example: in Geneva, for official measurements of the ISM, the 2003-1011 average is 10% above the 1980-2002 average, which is probably an extreme situation.

However if you have averages of years mostly after 2000, you can let this value to null.

## Details

### P50 determination - Kind of data

The simulation result is closely related to the Meteo input used for the simulation. This may be of different kinds, which has to be entered as the parameter "Kind of data":

•If the data are representative of an average over several years ("Monthly averages" or "TMY, multi-year"), the simulation result should be considered as an average, and generally corresponds to P50 (mean value of the Gaussian).

However PVsyst gives the opportunity of taking a specified climate change into account: this will displace the mean value P50 of the Gaussian with respect to the simulation result. This is useful for interpreting simulations performed with old average data (Meteonorm, PVGIS classic, etc), which are known to be lower than the present climate.

•If the data are for a specified year ("Own measured", or "Specific year"), these cannot be considered as representative of the P50 value. In absence of further information you cannot determine a reliable P50-P90 indicator. But if you have some information about the usual average of the site, you can introduce an estimation of the deviation of this particular year with respect to the average. Again, this will displace the P50 value with respect to the simulation result.

Note that the software will determine automatically the kind of data for most known sources.

### Variability determination

The annual variability (sigma value) will be dominated by the meteo year-to-year variability. This information is not commonly available.

- | A report of Pierre Ineichen (2011) gives some evaluations for about 30 sites in the world. PVsyst proposes default values according to these data. |

- | The new version of Meteonorm 7.2, 7.3 and 8.0 provide this information for your site (see the "site definition" dialog, page "Monthly Meteo"). |

- | Several meteo data providers can now deliver multi-year meteo data (sets of 15 to 25 years), that you can directly import in PVsyst (for example Solargis, 3-Tiers Vortex, Soda-Helioclim, or other). If you avail of such meteo data for your site, you can calculate the RMS of the annual GlobInc distribution. You have a tool for doing this in PVsyst: please use "Databases > Compare Meteo Data", and here choose the corresponding MET files for different years. You have an option "Histo and Probabilities" which shows the Gaussian distribution, average and RMS. |

Additional uncertainties in the simulation process could eventually be taken into account. These deviations should represent random variability of the uncertainty from year to year, not the absolute uncertainty !

- PV modules model and parameters (the main uncertainty after Meteo)

- Inverter efficiency | (negligible) |

- Soiling and module quality loss (highly depending on the site conditions)

- Long term degradation | This is not compatible with the P90 evaluation concept. |

We don't know how to handle this in the present time. |

- Custom other contributions

All these random contributions will add quadratically, giving a global standard deviation which may be applied for constructing the final Gaussian distribution function, and give estimation of the P90 or any other Pxx indicator.

This is for very special uses: in usual situations, all these values may be let to null values.

NB: In the Gaussian distribution function, P90 represents a shift of -1.28 sigma, P95 => -1.64 sigmas, and P99 => -2.35 sigmas.

PVsyst shows a graphical representation of your choices, either as a Gaussian probability distribution for several years, or as the corresponding cumulative distribution (the integral of the gaussian).

On this example, the simulation was performed using a specific year, which was supposed to be -3% below the yearly average. Therefore the P50 value is higher. A positive climate evolution would have the same effect.

Playing with the uncertainty parameters is highly instructive about the representativity of the simulation result for the future years. It is interesting to observe that according to your interpretation of the simulation result (i.e. E_Grid, fixed), the forecast productions distribution may move around your simulation result !

## P90 estimations for monthly or daily values

The P50-P90 statistical estimations are based on yearly values. Defining P90 for hourly or daily values (or even for monthly accumulations) doesn't make sense !

When the variations of annual meteo data is of the order of 3-4% (RMS), the variability of monthly data from year to year is much higher, and defining a probability profile for each month will give erratic results.

By the way the probability profiles for the determination of P90 are statistical estimations, which should be based on significant weather series (at least 15-20 years of meteo data).

But we don't avail of such generic data for monthly values, and this would be very dependent on the climate and the season.

If you want to do such evaluations, you should find monthly meteo data of 15 years or more for your site, and evaluate the probability distribution month-by-month.

Correction of Hourly values

For defining P90 hourly values, some people think to simply diminish the yearly hourly results by the ratio of the yearly yields P90 / P50.

This is not correct, as the behavior of your system will be exactly the same for clear conditions. The eventual P90 "correction" would affect the distribution and frequency of bad weather conditions, not the absolute yield of each hour.

Some meteo data providers propose Meteo Time series corresponding to P90 (or other Pxx). We don't know how these data are elaborated, and we don't know the significance of such data.