*2.5. Error Measurements*

Three error metrics are used to evaluate the performance of the ANN model when predicting photovoltaic power, and also to compare the two datasets used on each of its input variables: mean bias error (MBE), root mean square error (RMSE), and normalised root mean square error (nRMSE). They are defined using the three following equations.

$$MBE = \sum\_{i=1}^{N} \frac{X\_i - Y\_i}{N} \tag{2}$$

$$RMSE = \sqrt{\sum\_{i=1}^{N} \frac{\left(X\_i - \mathbf{y}\_i\right)^2}{N}} \tag{3}$$

$$nRMSE = \frac{\sqrt{\sum\_{i=1}^{N} \frac{\left(X\_i - Y\_i\right)^2}{N}}}{Y\_{\text{max}}} \tag{4}$$

Where *Xi* is an individual value from one of the variables of the GDAS dataset (estimations), *Yi* is the corresponding value from the monitoring dataset (observations), *Ymax* is the largest value of the entire monitoring dataset (43.53 ◦C for temperature, 1045.48 W/m<sup>2</sup> for solar irradiation and 848.66 kW for PV production), and *N* is the number of data hours (sample size).

The MBE provides a measurement of the general bias of a given variable, while the RMSE provides more information about individual discrepancies with reality for a large set of estimations. Both of them compute error values in physical units. The nRMSE is a nondimensional version of the RMSE. It is useful for evaluating the relative performance between unrelated magnitudes. In the case of power generation systems, it can be used to directly compare the output errors from modelled systems with different nominal capacities [16].
