We compare 1 min averaged forecast results for DNI for 3-15 min time horizons. A forecast value is computed for each cloud fraction Xi and each time horizon Th, j :
Ух, (t + Th, j) = DNIcs(t + Th, j) • (1 – Xi) where DNIcs (t) is the clear-sky model for DNI.
|
FIGURE 15.11 Main image-processing steps. Left: original 8-bit image in grayscale; middle: image projected to a rectangular grid using image-to-sky mapping and velocity fields computed by the PIV algorithm; right: cloud decision image. Notice the 7 “ladder” elements used for the forecasting and how they are aligned with mean cloud velocity. |
|
TABLE 15.3 RMSE Computed for 3- |
-15 min Forecasting Horizons (kW/m2) |
N |
|||||||
|
Forecast horizon |
Dull Persistence |
X1 |
X2 |
X3 |
X4 |
X5 |
X6 |
Improvement w. r.t. Dull persistence (%) |
|
|
3 |
0.279 |
0.258 |
0.28 |
0.313 |
0.333 |
0.347 |
0.361 |
7.5 |
|
|
4 |
0.301 |
0.213 |
0.242 |
0.293 |
0.321 |
0.343 |
0.345 |
29.2 |
|
|
5 |
0.326 |
0.236 |
0.208 |
0.274 |
0.307 |
0.334 |
0.335 |
36.2 |
|
|
6 |
0.36 |
0.283 |
0.224 |
0.25 |
0.296 |
0.323 |
0.331 |
37.8 |
|
|
7 |
0.379 |
0.312 |
0.261 |
0.242 |
0.278 |
0.317 |
0.326 |
36.2 |
|
|
8 |
0.39 |
0.328 |
0.279 |
0.269 |
0.277 |
0.308 |
0.325 |
31.0 |
|
|
9 |
0.403 |
0.346 |
0.316 |
0.294 |
0.305 |
0.312 |
0.33 |
27.1 |
|
|
10 |
0.415 |
0.368 |
0.338 |
0.317 |
0.325 |
0.327 |
0.341 |
23.6 |
|
|
11 |
0.424 |
0.392 |
0.355 |
0.337 |
0.337 |
0.332 |
0.349 |
21.7 |
|
|
12 |
0.436 |
0.41 |
0.377 |
0.355 |
0.35 |
0.345 |
0.353 |
20.9 |
|
|
13 |
0.455 |
0.417 |
0.398 |
0.374 |
0.37 |
0.366 |
0.36 |
20.9 |
|
|
14 |
0.463 |
0.421 |
0.413 |
0.394 |
0.387 |
0.385 |
0.373 |
19.4 |
|
|
15 |
0.467 |
0.433 |
0.42 |
0.412 |
0.401 |
0.402 |
0.392 |
16.1 |
|
|
Note: Boldfaced numbers represent best RMSE with respect to time horizon. |
Table 15.3 shows the results for June 5, 2011. The values in it show that there is a clear trend correlating distance from the Sun with the best forecast horizon. Variables representing grid elements further away from the Sun are more useful for predicting DNI at longer time horizons. Comparison with the dull-persistence model (leftmost column) shows that the most improved forecasts occur for 5 min ahead, but the wind-ladder sector approach shows substantial improvement over persistence for 15 min ahead.
Results for this novel method of sky-image solar forecasting are very encouraging despite the usual difficulties in generalizing the performance of cloud-identification schemes. Previous work using sky imagers highlighted the intrinsic difficulties in achieving robust cloud classifications (Long et al., 2006; Crispim et al., 2008; Huo & Lu, Oct 2009), in particular for images with large amounts of glaring. We experienced similar difficulties, but we anticipate that improved cloud classification of images, together with the incorporation of stochastic-learning for translation-error reduction, will contribute significantly to improvement in forecast accuracy at short-term horizons.
A more advanced forecasting algorithm, one combining the methodology to extract information from sky images with more advanced machine learning such as ANN and GA-optimized ANN, would further improve forecasting, as we have seen.
