Several energy management applications rely on accurate photovoltaic generation forecasts. Common metrics like mean absolute error or root-mean-square error, omit error-distribution details needed for stochastic optimization. In addition, several approaches use weather forecasts as inputs without analyzing the source of the prediction error. To overcome this gap, we decompose forecasting into a weather forecast model for environmental parameters such as solar irradiance and temperature and a plant characteristic model that captures site-specific parameters like panel orientation, temperature influence, or regular shading. Satellite-based weather observation serves as an intermediate layer. We analyze the error distribution of the high-resolution rapid-refresh numerical weather prediction model that covers the United States as a black-box model for weather forecasting and train an ensemble of neural networks on historical power output data for the plant characteristic model. Results show mean absolute error increases by 11% and 68% for two selected photovoltaic systems when using weather forecasts instead of satellite-based ground-truth weather observations as a perfect forecast. The generalized hyperbolic and Student's t distributions adequately fit the forecast errors across lead times.
Figures & tables
Figure 1: Inputs/outputs of the plant characteristic model on the time axis.
Figure 2: Plant characteristic model: ensemble of MLP .
Figure 3: Location of selected PV systems and the SOLRAD irradiance observation network.
Figure 4: Pre-processed AC power data from the selected PV systems with training and test data split.
System
33
1423
both
Corr.
P
S
P
S
P
S
GHI
0.91
0.88
0.93
0.97
0.91
0.89
s
0.79
0.86
0.87
0.96
0.81
0.87
Temp.
0.40
0.54
0.23
0.29
0.34
0.34
pt−1
0.90
0.90
0.93
0.93
0.91
0.91
pt−24
0.80
0.89
0.93
0.98
0.82
0.92
Table 1: Pearson (P) and Spearman (S) correlation of input features to PV power output.
Figure 5: Spearman correlation of input features to the AC power output of both PV systems.
Figure 6: Impact of hidden layer width on the R2 score for system 33. The red indicator shows the selected width, highlighting the start of the yellowish plateau.
Figure 7: Errors of the plant characteristic model with a forecast at 23:00 of system 33. Orange curves show the fitted normal distribution in the probability density plots.
Plant
Weather
Combined
System
Power
GHI
Temp
Power
W/kWp
W/m2
\SIUnitSymbolCelsius
W/kWp
MBE
33
-0.12
20.68
3.88
18.34
1423
-5.53
12.66
-1.02
6.57
MAE
33
28.12
39.94
3.97
47.28
1423
28.04
22.74
1.61
31.16
Table 2: Error metrics for 24 leads starting at 6:00 UTC.
Figure 8: Errors of the plant characteristic model with a forecast at 22:00 of system 1423. Orange curves show the fitted normal distribution in the probability density plots.
Figure 9: Errors of the weather forecast model with a forecast at 23:00 of system 33. Orange curves show the fitted normal distribution in the probability density plots.
GHI in W/m2
Temperature in \SIUnitSymbolCelsius
Station
MBE
MAE
MBE
MAE
System 33
20.68
39.94
3.88
3.97
System 1423
12.66
22.74
-1.02
1.61
Albuquerque
11.65
27.89
0.77
1.41
Bismarck
14.00
31.05
0.26
1.34
Hanford
6.04
20.17
-1.88
2.10
Table 3: HRRRv4 forecast accuracy at SOLRAD network stations and selected PV systems with 24 leads at 6:00 UTC.
Figure 10: Errors of the weather forecast model with a forecast at 23:00 of system 1423. Orange curves show the fitted normal distribution in the probability density plots.
Figure 11: Errors of the combined model with a forecast at 23:00 of system 33. Orange curves show the fitted normal distribution in the probability density plots.
Figure 12: Temporal correlations of lead distance using SOLRAD stations locations forecasts for every 6 hours
Figure 13: Errors of the combined model with a forecast at 22:00 of system 1423. Orange curves show the fitted normal distribution in the probability density plots.
Normal
Student’s t
Generalized Hyperbolic
Lead
K-S
C-M
K-S
C-M
K-S
C-M
6
0.615
0.445
0.591
0.419
0.576
0.474
7
0.160
0.092
0.090
0.158
-
0.009
8
0.735
0.866
0.735
0.866
0.597
0.811
9
0.634
0.612
0.590
0.596
0.864
0.845
10
0.000
0.000
0.049
0.104
0.534
0.511
Table 4: Goodness-of-Fit of different distributions for system 1423 showing the p-values of the Kolmogorov-Smirnov (K-S) and Cramér-von Mises (C-M) test at 22:00 local time.
Figure 14: Errors of the weather forecast model for air temperature with a forecast at 6:00 UTC.
Figure 15: Q-Q plots on empirical data against fitted distributions for the forecast at 22:00 for system 1423.
Solar power forecasting predicts photovoltaic generation and irradiance from weather, imagery, plant data, and recent output to support reliable grid and energy decisions.