In this study, a new solar photovoltaic (PV) panel output power model is proposed. The model is constructed as a function of ambient temperature and solar radiations for two types (fixed panel and sun tracking panel) of PV systems. The proposed models are tested and verified on the Renewable Energy Research Home (RERH) system that was installed at the Anadolu University campus in Eskisehir, Turkey. The model is deliberately constructed for the winter season, where cloudliness, rain and snow constitute more challenging conditions for modeling. The developed model outcomes are compared to the outputs of state of the art methods that use global solar radiation and temperature data. A total of eight algebraic models are constructed for the purpose of depicting the solar radiation-to-electric power behavior. It is observed that even the least successful one of these eight variants are performing better than the most accurate method in the literature. It is argued that mathematical incorporation of the proposed novel hysteresis functions to the solar radiation-to-power conversion curves results in a richer class of functions and causes a significant accuracy improvement on the mathematical power generation model, even for the most challenging season of winter.