In this study, we have performed an analysis of potential irradiation increase across Europe, derived from moving photovoltaic (PV) modules to a horizontal position during cloudy and overcast situations. The motivation of research is that PV technology has expanded outside countries endowed with high solar irradiation and it is nowadays present in high-latitude regions and areas with frequent cloud cover. Unlike concentrating solar technologies, PV panels can make use of both beam and diffuse irradiance. During cloudy or overcast situations, most of solar irradiance comes from the diffuse component, which approaches an isotropic behavior under those circumstances. Then, a PV panel facing the zenith would receive more irradiation than a PV panel following the Sun's path. In our approach, we have used data from several Baseline Surface Radiation Network stations. Results showed a yearly potential irradiation increase of 3.01% with respect to a reference single-axis tracking system (SATS) in the northern-most station. Values for other stations were correlated to climate. Thus, the sunniest station would increase its annual irradiation by 0.16% compared to a reference SATS. Daily irradiation increases of up to 19.91% were registered. Two predictive models were created to develop a SATS, which could determine in advance the optimum position of PV panels. Model 1, which was based on the persistence of irradiance, was designed to work real time in order to increase production. Yearly gains of up to 2.51% of irradiation were registered. However, Model 2 was developed to update production forecasts in the intra-day electricity markets so that PV plant owners can maximize their revenues. It is based on irradiance predictions from a numerical weather prediction service and underperformed current SATS.