4.1. Photovoltaic panels generation forecasting

In order to forecast the electricity produced by photovoltaic panels, we used input data from one PV power plant of 7.6 kW located in Giurgiu City, Romania, installed at a prosumer side on his building facade. PV generates electricity for the consumption of the prosumer, and when the consumption is lower than the PV output, the electricity is sent to the grid. For our experiments, data was recorded at 10 minutes interval, from January to December 2015 and includes the following attributes: ambient temperature, humidity, solar radiation, wind direction, wind speed and PV output (generated power), having more than 50,000 records.

First, we applied the ARIMA models and we calculated the error distribution, MSE, MAPE and R correlation coefficient (Table 4).

From our observations, the correlation coefficient indicates a strong relationship between solar radiation and the PV power forecast. This close dependence showed that regression models are appropriate for this time series. The best results were obtained with ARIMA model where the accuracy is 96.5% that indicates that the model can be used in PV panels generation forecast.

We consider a second method based on feed-forward neural networks. Therefore, we trained and validated a set of ANN in Matlab using Levenberg-Marquardt (LM), Bayesian Regularization (BR) and Scaled Conjugate Gradient (SCG).

For ANN architecture, we analyzed various settings regarding the number of neurons per layer, number of hidden layers and training algorithms. After several tests, we chose the following architecture: the input layer with 5 neurons (ambient temperature, humidity, solar irradiation, wind direction and wind speed) 60 neurons on a hidden layer and a single output (the energy produced).


Table 4. Stochastic models results in case of PV generation forecasting.

For training, validating and testing: we have allocated 70% of the records for the training process, 15% for the validation process and 15% for the testing process. For training errors, we used the mean square error (MSE) by applying an error normalization process by configuring the normalization parameter to "standard". Thus, output parameter values were standardized, ranging from [�1, 1].

Taking into account the seasonal variations of the influence factors in Romania, we built artificial neural networks based on the three algorithms for each month and we compared the results in Table 5.

Comparing the ARIMA and ANN results, we consider that the most efficient approach is to use ANN on monthly data sets, which leads to excellent accuracy for every analyzed month. We also found that in almost 70% of cases, BR algorithm has a better generalization than LM or SCG algorithms. In 30% of cases, the highest accuracy was obtained with LM algorithm.
