*3.2. Analysis of PV Power Predictions*

Figure 5 shows photovoltaic power outputs for the same two weeks used in Figure 4, again including real (Monitoring) and estimated (Scenarios 1–3) signals, and the differences between them. Output values for the three analysed scenarios are included, as well as values from the monitoring dataset for reference. Again, temperature graphs are omitted.

A comparison between solar irradiation inputs and PV outputs for four of the randomly chosen days is shown in Figure 6. They cover situations of good and bad matching between monitoring and GDAS solar irradiation for both 2012 (first and second subplots, corresponding to days of March and April 2012) and 2013 (third and fourth subplots, for days of August and October 2013).

**Figure 5.** Comparison of PV power outputs for manually chosen weeks.

Table 3 shows the error results for photovoltaic power predictions for the three scenarios. The same considerations from Table 2 apply here. In this new table, only the random days and manual weeks are used. The entire temporal span of the study is not considered in order to avoid including data values already used during the training of the ANN model.

The performance of the predicted PV output variable is reasonably good on all scenarios and for both samples of random days and manual weeks. As with the input variables, MBE results for power predictions are much closer to zero than their RMSE counterparts, meaning that power biases for individual days and hours tend to be nullified for more complete periods of time. RMSE errors on power production are lower than 25 kW (first scenario) and 85 kW (second and third scenarios). The real magnitude of these errors is easier to evaluate when compared with the 960 kWp of peak production installed for the monitored PV system, and the actual maximum value of PV production from the monitoring dataset, i.e., 849 kW. In fact, nRMSE values are lower than 3% for the first scenario, and lower than 10% for the other two, with maximum standard deviation values of 5%.

Graphs of power outputs and irradiation inputs for the 22 randomly chosen days tested (as well as those of the two manually chosen weeks) show almost identical patterns. This can be seen in the examples in Figure 6, in which power prediction curves from the second and third scenarios perfectly match the solar irradiation curve predicted by GDAS, while the power prediction curve from the first scenario replicates the solar irradiation curve provided by the monitoring dataset. This behaviour is to be expected due to the high correlation between the solar irradiation and the power output of

a PV system [16,32]. Key instants on the daily behaviour of PV production curves (starting, peak, and ending production hours) for the monitoring data match closely with the predictions of the ANN model in all three scenarios, in the same fashion as with solar irradiance.

**Figure 6.** Comparison of irradiation and power prediction. (**a**) Monitoring and GDAS solar irradiation for four randomly chosen test days. (**b**) Monitoring and scenarios PV power prediction for the same four days.


**Table 3.** Error metrics of PV power outputs.

Power outputs from the first scenario are most similar to measurements from the monitoring dataset, with very low errors (mean RMSE lower than 25 kW) and almost identical curves for all random days and manual weeks. These similarities are to be expected, as the neural network model uses monitoring data for both training and testing on this first scenario. The performance of PV predictions from the second and third scenarios are also quite similar, in terms of both error metrics (except mean MBE values for manual weeks) and graphics. This is a remarkable result, as the ANN models from these scenarios are trained using weather inputs from different datasets, even when they both use the same weather data to test their performances. Although the performance of the second and third scenarios is not as good as that of the first one, it is still quite significant, with mean bias errors of less than 14 kW below the real outputs, and mean nRMSE errors lower than 10% of the maximum power output measured for the entire study span.

As with solar irradiation, it is sensible to compare results for PV production with those available in the literature. In [33], next-day forecasts of power outputs from a 264 kWp PV plant in the North of Italy were generated using an ANN model, trained with the error back-propagation method, and coupled with a clear sky solar radiation model. The error analysis took into account three different significant days with sunny, partially cloudy, and cloudy weather conditions, obtaining nRMSE values of 12.5%, 24%, and 36.9% respectively. In [32], nRMSE values in the 10.91–23.99% range were achieved when predicting power output forecasts in a horizon of 1–24 h for the same PV system as that modelled in the present study (a 960 kWp installation located in the South of Italy), using an Elman ANN model. In [34], a 1 MWp PV plant in California was modelled using a feed-forward ANNs model and a genetic algorithms/ANN (GA/ANN) hybrid model, among others. The reported RMSE errors for forecasts 1 and 2 h forward were 88.23–142.74 kW for the ANN model, and 72.86–104.28 kW for the GA/ANN model. The reported nRMSE values were computed using a different definition, thus making comparisons with the present study unreliable.

The nRMSE values from Table 3 for random days in the second and third scenarios are equivalent to those of the best-performing cases in [33] (sunny days) and [32] (one-hour-horizon forecasts). The corresponding RMSE values are slightly lower than those obtained in [34] using their ANN model for a forecast horizon of one hour, and slightly worse than those from their GA/ANN model. It is worth noting that no distinctions are made between prediction performance for sunny or cloudy days in the present study. However, the selection of test days ensures that both high-irradiation days (typical of the summer season and clear sky conditions) and low-irradiation days (typical of the winter season and clouded sky conditions) are represented in the random test sample. Also, no distinctions between forecast hourly-horizons are made here, but the nature of the GDAS dataset implies that all data belong to a forecast horizon from 0 and up to 5 h, as explained in the Data Preprocessing section. The modelled PV system presented in [34] is not identical to the one in the present study. However, the peak output productions from both installations are similar enough, so at least a soft comparison of dimensional metrics like the RMSE can be made.
