1. Uncertainty for solar products assessment and
benchmarking
J. Polo, L. Ramírez, L.F.Zarzalejo, L. Martín, A. Navarro
CIEMAT (Energy department – Solar Platform of Almería)
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

2. Uncertainty parameters
Parameters based on deviation of data values (careful with notation)
n
( yi − g i )
MRE = ∑ × 100
 Mean Relative Error (MRE) n
gi
∑ ( gi − yi ) / n i =1
i =1
 Mean Bias Error (MBE) MBE = n
× 100
∑ gi / n
n
i =1
∑ ( gi − yi )2 / n
 RMSE RMSE = i =1
n
× 100
∑ gi / n
i =1
Parameters based on deviation of distribution functions
 KSI and OVER (Integral of KS test complete and
over critical value)
 KSE KSE = ( KSI × w1 + OVER × w2) / 2
RIO = ( RMSE + KSE ) / 2
 RIO
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

3. Daily analysis (Uncertainty parameters)
KSI OVER
KSE = ( + )/2 RIO = ( RMSE + KSE ) / 2
2 1000
Statistical uncertainty parameters dor daily irradiation Uncertainty parameters for daily irradiation
20 100
MRE RMSE
MBE 90 IKS
15 RMSE OVER
80
KSE-p
RIO-p
70
Uncertainty parameter (%)
10
60
5 50
40
0
30
20
-5
10
-10 0
Caceres Madrid Murcia Coruña Valencia Santander Valladolid Caceres Madrid Murcia Coruña Valencia Santander Valladolid
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

4. Daily analysis (KS Test)
0.1
Coruña
0.09 Caceres
Madrid
0.08
Murcia
Santander
0.07
Distances between CDFs
Valencia
0.06 Valladolid
0.05
0.04
0.03
0.02
0.01
0
0 2000 4000 6000 8000 10000 12000
Rangos de rad
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

5. Hourly analysis (Uncertainty parameters)
IKS OVER
KSE = ( + )/2 RIO = ( RMSE + KSE ) / 2
1000 2
Statistical uncertainty for hourly irradiation Uncertainty parameters for hourly irradiation
30 100
RMSE
MRE
90 IKS
25 MBE
RMSE OVER
80
KSE-p
20 RIO-p
70
Uncertainty parameter (%)
60
15
50
10
40
5 30
20
0
10
-5 0
Murcia Caceres Madrid Valladolid Santander Valencia Coruña Murcia Caceres Madrid Valladolid Santander Valencia Coruña
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

6. Hourly analysis (KS Test)
0.1
Coruña
0.09
Caceres
0.08 Madrid
Murcia
0.07
Distances between CDFs
Santander
0.06 Valencia
0.05 Valladolid
0.04
0.03
0.02
0.01
0
0 200 400 600 800 1000 1200
Irradiation (Wh m-2)
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

7. Towards standardization: open issues for
discussion
 Solar Radiation Product uncertainty: users require one number
(Radiation ± U) . Candidates: RMSE, MBE, relative error…
Problems with normalization.
 Model assessment: we look for more information than uncertainty.
strengths and shortcomings of models is also required.
Candidates: K-S Test in addition to uncertainty measures MBE,
RMSE, deviations at different solar elevation angles, … are useful
for this purpose.
 Benchmarking of models: We should know a priori the capabilities
of different models and we want to compare their response under
the same conditions.
Candidates: RIO parameter compiles KS test and RMSE
information in one single parameter.
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007

8. Future activity
Benchmarking exercise on one selected pixel for
one year of hourly global irradiation?
Elaboration of a guide for uncertainty (MESoR)?
4th Meeting IEA SHC Task 36 Hamburg 23-25 Oct 2007