# A Review on Neural Network Based Models for Short Term Solar Irradiance Forecasting
## 2 The Impact Factor of Solar Power Forecasting
### Model Performance Metrics  
The performance evaluation metrics are useful throughout the model development process because it is impossible to analyze how effectively deep learning models would perform without the use of metrics for comparison [6]. However, performance can be affected by many factors, such as the forecasting horizon, model parameters, and site-specific meteorological circumstances. Specifically, the overall performance is assessed based on a comparison between actual and forecasted solar irradiance. The metrics used will provide feedback in terms of forecasting accuracy, allowing models to be fine-tuned to achieve a target degree of precision; a lower score indicates more precise forecasting. Commonly used statistical evolution metrics for evaluation purposes include the following:  
* Mean Absolute Error (MAE): this metric demonstrates the mean of the absolute errors among the actual GHI values and the anticipated values, and it provides equal weight distribution to all data inconsistencies, which can be shown in Equation (1) [74]: \[\text{MAE}=\frac{1}{N}{\sum_{i=1}^{n}}{\left|{Ga_{i}-Gp_{i}}\right|}\] (1) where \(Ga_{i}\) and \(Gp_{i}\) denote the actual and predicted GHI values, respectively, while the total number of data points is represented by n.
* Mean bias error (MBE): This metric evaluates the established mean bias of the forecasting model. The MBE adjusts the deviation by subtracting the positive from the negative, as shown in Equation (2). It is considered an unreliable method for performance evaluation; however, it does provide an adequate indication of whether a model is over- or under-estimated [74]. \[\text{MBE}=\frac{1}{N}{\sum_{i=1}^{N}}{\left({Gp_{i}-Ga_{i}}\right)}\] (2)* Mean square error (MSE): This metric is the mean calculation of square differences between the actual and forecasted solar irradiance levels, as shown in Equation (3). Therefore, larger disparities occur [75]. \[\text{MSE}=\ \frac{1}{N}{\sum_{i}^{n}\left({G{p_{i}}-Ga_{i}}\right)^{2}}\] (3)
* Root mean square error (RMSE): This metric is the calculation of the square root of the average squared variances between actual and forecasted solar irradiance values. RMSE is recognized as being one of the most trusted ways to measure performance because it helps to identify and eliminate data outliers. The metric is expressed via Equation (4) [76]: \[\text{R}=\sqrt{\frac{1}{N}{\sum_{i}^{n}\left({G{p_{i}}-Ga_{i}}\right)^{2}}}\] (4)
* Mean absolute percentage error (MAPE): this metric is the relative average value between MAPE and MAE, which is obtained by dividing the differences between each actual and forecasted observed value by the actual observed value, as shown in Equation (5) [77]. \[\text{MAPE}=\frac{1}{N}{\sum_{i=1}^{N}/\frac{G{p_{i}}-Ga_{i}}{Ga_{i}}}/\] (5)
* Normalized RMSE (nRMSE): in general, nRMSE is used to identify overall deviance in larger datasets, as shown in Equation (6) [77]. \[\text{nRMSE}=\ \frac{\sqrt{\frac{1}{N}{\sum_{i}^{n}\left({G{p_{i}}-Ga_{i}} \right)^{2}}}}{\overline{Ga_{i}}}\] (6)
* Correlation coefficient (R): this metric measures the linear correlation between actual and forecasted solar irradiance [78], and it is calculated as shown in Equation: \[\text{R}=\frac{\sum_{i}^{n}\left({Ga_{i}}-\overline{Ga_{i}}\right)\left({G{p_ {i}}-\overline{G{p_{i}}}}\right)}{\sqrt{\sum_{i}^{n}\left({Ga_{i}}-\overline{ Ga_{i}}\right)\sum_{i}^{n}\left({G{p_{i}}-\overline{G{p_{i}}}}\right)^{2}}}\] (7) \(\overline{G{p_{i}}}\) and \(\overline{Ga_{i}}\) represent the average of forecasted and actual GHI, respectively. * Forecast skill score (FS): the FS score compares the performance of the forecasting model and the benchmark or persistence model, as shown in Equation (8): \[\text{FS}=1-\frac{\text{RMSE}_{\text{model}}}{\text{RMSE}_{\text{simple model}}}\] (8)  
In terms of accuracy, an optimal forecast model will achieve an FS score of 1, whereas a model that exhibits the same forecast error as the benchmark model has a value of 0. The FS score will produce negative results with a larger forecast error [79].