P99 Value for the Nth Year

[Gmontano]

Apologies if the answer is implied or present in existing documentation. 

In my PVSyst report under 'P50-P90 Evaluation' section - I have the following data:

Weather Data:
Year-to-year Variability: 4.9%

Global Variability (Weather Data + System):
Variability (Quadratic Sum): 5.2%

Annual Production Probability:
Variability: 3.11 GWh
P50: 60.13 GWh
P99: 52.88 GWh

For simplicity - assume no degradation.

From this report the first year the P99 value for my project is 52.88GWh. Though - what would be the "year-2 P99"?

This is an interesting question. Let X1 and X2 represent the production levels in the first and second years respectively. If X1 is 52.88GWh, then what is X2 such that I am 99% confident that I will produce at least X1 + X2 after 2 years.

I can assume that X2  ~ N(Mean, Variance) = N(60.13, 3.11^{2}), and assuming it is independent from X1, infer the distribution of (X1 + X2) ~ N(2*60.13, 2*3.11^{2}).

While the maths makes sense - I am unsure the present assumptions, and therefore, have small confidence in the numbers I am calculating for the intended purpose.

I appreciate your help - thank you very much,
Gus

Edited October 7 by Gmontano

[dtarin]

For a single year, σ = 3.11. For two consecutive years, σ = σ / √2

Var( X̄ ) = ( 1/n )^2 * Var( X₁ + X₂ + ... + Xₙ ) = ( 1/n )^2 * ( nσ² ) = σ² / n

 

[André Mermoud]

The variance of the meteo data multi-year distribution is supposed to be the same for any future year.

Therefore the ratio P99/P50 remains the same whatever the year.

You can simply calculate P99 (YearN) = P50(YearN) * P99/P50 (Year0)

[dtarin]

For any single year that is the case. For multiple years, the uncertainty due to annual variability decreases, so this parameter needs to be separated out and used with the equation in my previous post, and then added to the other uncertainty quantities in full. My example was not quite correct in this regard. 

[dtarin]

1 hour ago, dtarin said:

For any single year that is the case. For multiple years, the uncertainty due to annual variability decreases, so this parameter needs to be separated out and used with the equation in my previous post, and then added to combined with the other uncertainty quantities in full. My example was not quite correct in this regard.