Intra-hour Forecasts of Solar Power and Ramp Events

In this study an adjusting post-processing approach is implemented for improving intra-hourly forecasts of solar power and ramp events of PV solar power systems at different locations in the United States. This study also serves as an out-of-sample test to evaluate the performance of the adjusting approach with different locations and timescales. Thus, various individual intra-hourly forecasts of solar power are combined and adjusted by applying the adjusting approach. Both point and probabilistic forecasts of solar power are included. After that, solar power ramp event forecasting by the adjusting approach is carried out.

solar power forecast.

Data Description
The data description and the specifications of PV solar systems are presented in Table 1, the data were acquired from the National Renewable Energy Laboratory, NREL [1].Another dataset of lower temporal resolution with hourly observations of solar power is also included in the rightmost column of Table 1.
The latter dataset is from Australia [2], which was previously used for the proposed adjusting approach to improve the hourly forecasts of solar power and 1. DATA DESCRIPTION ramp events, the results were reported in [3,4].
The datasets of PV systems at the U.S. sites have higher temporal resolutions, wherein the original resolutions are 15-min for Golden, CO, 5-min for Cocoa, FL, and Eugene, OR.The U.S. data is adopted for evaluating the adjusting approach with intra-hour forecasts, besides of being as an out-of-sample test of the forecasting accuracy [5].To obtain a consistent duration of the ramp rates, 3 durations are chosen (15-min, 30-min, and 60-min), and these durations are also the rolling windows for intra-hour forecasts of solar power and ramp events.It can be noticed in Using the data from the U.S. sites with 3 forecast horizons (15, 30, and 60-min) for each site of the available sites, the number of case studies is 9.
The U.S. data are associated with measurements of several weather variables listed in Table 2.

Methodology
The adjusting approach, as described in the former published paper [3], is now modified to include some adjustments for determining intra-hourly forecasts of solar power and ramp events.The procedure is depicted in Figure 1.
Remark The advancements of High-Resolution Rapid Refresh (HRRR) model, which is run by the National Oceanic and Atmospheric Administration (NOAA), made it possible to produce hourly forecasts of weather variables.
However, powerful computing equipment and big data tools are required for modeling solar ramp events efficiently with those HRRR forecasts in terms of storage size and computation speed.Moreover, the weather forecasts are not yet available in intra-hourly timescale, and despite the high accuracy of HRRR weather forecasts, some of the extreme ramp events are still unpredictable [6,7].
Since this study is focused on very short-term forecasts with U.S. data for horizons up to 1-hour, the available meteorological measurements in the U.S. may be used as an alternative to the weather predictions in the Australian data, which were used for hourly forecasts.
Statistical time-series models are employed to generate the individual forecasts of solar power, including ARIMA, NAR, ANN, and Extreme Learning Machine (ELM).
At the combining stage of the adjusting approach, as shown in Figure 1, the double target-horizon forecasts are combined with target-horizon forecasts, for which the adjusting is performed.Some available meteorological measurements are assimilated in the adjusting approach.The combined meteorological data are the temperature of PV panel, the relative humidity, and the direct normal irradiance (DNI).The intra-hourly information of the cloud cover can be delivered by the DNI [8].

Results
The performance of the individual forecasts are evaluated by using the RMSE, MAE, and MBE, for the 3 forecast horizons of the 3 sites of the U.S.    The simple average method is also employed to combine the individual forecasts for a comparison with the intra-hourly combined forecasts of solar power

RESULTS
by applying the adjusting approach.The diagram of the combining method by the simple average is shown in Figure 2.

Target-horizon forecasts
Combining   As expected, the combined forecasts even by the simple average outperform the individual forecasts, and an additional improvement is achieved by applying the adjusting approach.From the last row in Table 5, the average RMSE improvement of the combined forecasts (RMSE=0.0310)from the adjusting approach is about 16% over the combined forecasts (RMSE=0.0368)by the simple average and 44% over the persistence forecasts (RMSE=0.0550).A graph of average improvements of the combined forecasts by the adjusting approach over  The intra-hourly combined forecasts from the adjusting approach for different locations and timescales are also evaluated by the DM test [9].Table 6 3. RESULTS indicates the adjusted combined forecasts outperform all other time-series forecasts, as demonstrated by the DM test, which evaluates the significant accuracy differences of the adjusted combined forecasts with respect to other forecasts.As shown in Table 7, the AnEn probabilistic forecasts are used to quantify the uncertainty of the combined forecasts from two combining methods -the simple average and the adjusting approach.The uncertainty of the combined forecasts by the adjusting approach is also quantified by the ensemble-based probabilistic forecasts, which are provided in the rightmost column of the table.
Table 8, presents the evaluation of intra-hourly probabilistic forecasts of solar power by using CRPS instead of pinball as an evaluation metric for the  probabilistic forecasts (PB=0.0080)by the adjusting approach over the EnAn of adjusting approach (PB=0.0091)and the EnAn of simple average (PB=0.0113)are 12% and 29% respectively.It should be noted that the average improvement of (PB=0.0080) is about 74% over the persistence probabilistic forecasts (PB=0.0311).

RESULTS
Forecasting of solar power ramp events is also carried out with these intrahourly data at sites in the U.S. Table 9 shows the statistics of solar power ramp rates with different thresholds to define the ramp rate as high or low, we observed that the maximum ramp rate is 0.487 pu/dt occurs at the Cocoa, FL, site with a temporal resolution equalling to 30-min.In provirus study with the Australian data, the maximum ramp rate was about 0.8 pu/hr.The number of high-rate ramp events is reduced significantly by increasing the threshold.For instance, at threshold=0.4pu/dt, the total number of high-rate ramp events is 6 events only.Whereas, in the Australian data, when using the same threshold (T sh = The intra-hourly forecasting of solar power ramp events is conducted with two thresholds to define the high and low ramp events, |Rate| ≥ 0.1 pu/dt and |Rate| ≥ 0.2 pu/dt, as shown in Figure 4 and 5, respectively. Figure 6 illustrates the forecasts of solar power ramp events by implementing the classification techniques.The SVM and RF techniques achieve the most accurate forecasts.Since the combined forecasts of solar power ramp events by the adjusting approach (Diff.Index=79) are included as input variable in

Figure 1 : 3 5
Figure 1: Block diagram of the adjusting approach for intra-hour forecasts of solar power and ramp events

Figure 2 :
Figure 2: Block diagram of the simple average method for combining intra-hour forecasts of solar power and ramp events

Figure 3 :
Figure 3: Average improvements of the combined forecasts by the adjusting approach with respect to other forecasts probabilistic forecasts.Although the evaluating values of pinball and CRPS are different, the improvements by pinball and CRPS are almost the same.However, in terms of pinball (PB), the average improvements of the ensemble-based Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 25 October 2018 doi:10.20944/preprints201810.0593.v1

Figure 5 :
Figure 5: Forecasts of solar power ramp events with different evaluation metrics of high-rate ramp events, when |Rate| ≥ 0.2 pu/dt

Table 1 :
Data description and specifications of PV solar systems to the previously used high quality data of the PV site in Australia, which is only with hourly observations of solar power, and hence, not suitable for intrahour forecasts.If the missing values in the data of U.S. sites are neglected, this can impact the ramp events modeling and forecasting.Therefore, those missing values are interpolated to fill the temporal gaps in the solar power time-series.

Table 1
that the variability (i.e., standard deviation) of the U.S. data decreases as the data resolution becomes lower.However, the Australian data with only 1-hour resolution has the highest variability (st.div.=0.259).

Table 2 :
Measured weather variables that are associated with data of PV systems at the U.S.

Table 3 :
The individual intra-hourly forecasts of solar power sites (i.e., averaging each column), which are rearranged and represented by RM SE agg , M AE agg , and M BE agg in Table4.

Table 4 :
The aggregated evaluation of the individual intra-hourly forecasts of solar power The RMSE and MAE have the same trends, and they indicate that in some cases of the individual forecasts, especially at the shorter horizon (15-min), they do not always outperform the persistence forecasts.The ANN produces the most accurate forecasts (RMSE=0.0455)with an average RMSE improve-

Table 5
presents the combined forecasts of solar power by the simple average (Simple Average) and the combined forecasts (Adjusting Approach) by the adjusting approach.

Table 5 :
Individual and combined forecasts of solar power Average improvement of the combined forecasts by the adjusting approach over othter forecasts

Table 6 :
The DM test of the intra-hourly combined forecasts by the adjusting approach over

Table 7 :
Pinball of the intra-hourly probabilistic forecasts of solar power

Table 8 :
CRPS of the intra-hourly probabilistic forecasts of solar power

Table 9 :
Statistics of intra-hourly data of the solar power observations for solar power rampEvaluation of Solar Power Ramp Events Forecasts by Using Different Evaluation Metrics Figure 4: Forecasts of solar power ramp events with different evaluation metrics of high-rate ramp events, when |Rate| ≥ 0.1 pu/dt Index Percentage (%) Evaluation of Solar Power Ramp Events Forecasts by Using Different Evaluation Metrics Precision (%) Recall (%) Balanced Precision (%) F1 Score (%) Diff.Index