The response time of a photovoltaic plant is very short and its output power follows the abrupt change in solar irradiance level due to alternate shadow by clouds. Presence of shading may be quantified by a binary variable: sunshine number (SSN). Various logistic Markovian models of SSN dynamics are introduced and discussed in this paper, going from simple to more complicated model structures. Radiometric data measured at 15 s lag during 2010 in Timisoara (Romania) are used to illustrate their real-world performance. The models are useful for short term forecasting related e.g. to photovoltaic conversion control, including more complicated events like ramp-like switches between overcast and clear regimes. Importantly, presented models are not black-box forecasting tools. They contain physically interpretable structure which is advantageous both in developing, checking and improvement of the model itself, but also as a tool for characterizing various systematic properties of cloud shading. (C) 2014 Elsevier Ltd. All rights reserved.