One of the key aspects enabling the bulk integration of photovoltaic (PV) resources into the power grid is the short-term prediction of the maximum available power (from 100 ms to 5 minutes), and the quantification of the associated uncertainties. This is beneficial for the definition of robust control strategies able to account for the stochastic nature of this energy resource. We propose and validate a comprehensive method to assess the overall PV power uncertainties, even at operating conditions different from the maximum power point (MPP), i.e., to consider when power curtailment strategies are adopted on a controllable PV plant. The proposed gray-box modeling includes physical and data-driven sub-models that rely on measurements of the PV currents, voltages, and the module temperature, information normally available to the PV plant operator. Furthermore, we identify which sub-model is the most critical in terms of uncertainty, for different forecast horizons. Experimental results analyze the ability of the method to guarantee the target coverage probability while accounting for the uncertain nature of the PV resource. We show how modelling and forecasting information can be used to express the PV plant behaviour to a grid controller responsible for the safe operation of a microgrid.