What is the P50-P90 probabilistic production ?

[André Mermoud]

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.

From the version 6.11, you can now define P50-P90 estimators with the button "Miscellaneous tools" in the project's dialog.

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 Variance (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.

P50 determination

The simulation result is closely related to the Meteo input used for the simulation. This may be of different kinds:

- If the data are representative of an average over several years (like monthly averages or TMY), the result should be considered as an average, and 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 by 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, 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 by respect to the average. Again, this will displace the P50 value by respect to the simulation result.

Variability determination

The annual variability (sigma value) will be dominated by the meteo year-to-year variability.

Additional uncertainties in the simulation process should also be taken into account:

- 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

- Custom other contributions

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

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

 

Example of a PVsyst P50/P90 determination

 

PVsyst shows a graphical representation of your choices, either as a gaussian probability distribution for several years, or as the corresponding repartition function (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.

In thre program, playing with the uncertainty parameters is highly instructive about the representativity of the simulation result. It is interesting to observe that according to your interpretation of the simulation result (i.e. E_Grid, fixed), the forecats productions distribution may move around your result !

How can I get P90 estimations for monthly or daily values ?

If 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.

Therefore the P50-P90 statistical estimation doesn't make sense for monthly values. And a fortiory for daily values of course.

By the way the probablilty 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).

For yearly values, in absence of real long-term weather series, PVsyst proposes default RMS values according to very general estimations of some few sites.

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

If you want to do such evaluations, you should find meteo data of 20 years or more for your site, and evaluate the probablity distribution for each month.

Correction of 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 a clear day. The eventual P90 "correction" would affect the distribution and frequency of bad weather days, not the absolute yield of each hour.