The dramatic penetration of sustainable energy systems, including photovoltaic (PV) systems, has profoundly affected the stability and the reliability of the power system. Hence, determining the generation characteristics of PV systems has been becoming a crucial task in planning and dispatching the power system. However, since the generation of PV systems is profoundly impacted by the weather conditions, especially the irradiance and the temperature, producing a PV model, which performs well at various conditions, has been a challenging task for years. In this paper, we present a model to determine the PV generation characteristics by obtaining the current-voltage (I-V) curves of the single-diode model. First, the three key points, including the open-circuit point, the short-circuit point, and the maximum power point, are estimated from the historical data based on an improved regression model. After that, a new algorithm is proposed, which ensures the model always converges at any temperature and irradiance conditions. The proposed model is validated by comparing with recently published models and the measured data from the National Renewable Energy Laboratory, USA. Compared to previous numerical models, the proposed model is capable of determining the generation characteristics of PV systems at anomaly conditions (anomalously low irradiance and anomalously high irradiance) with high accuracy and fast speed. The validated results demonstrate the accuracy and the reliability of the proposed model in determining the generation characteristics of PV modules at real-time conditions.