Solar photovoltaics (PV), one of the most promising and rapidly developing renewable energy technologies, have evolved towards becoming a main renewable electricity source. They are termed variable energy resources since solar irradiance is non-dispatchable and intermittent in nature. This variability is a critical factor when predicting the available energy of solar sources. Secondary and tertiary control of microgrids is currently used to optimize power consumption and operational costs despite the variability of solar generation. Presently, tertiary controls optimize dispatch over large time scales (15 min – 1 hour). This dispatch optimization requires long term prediction of solar output. It has been shown through short-time measurement of solar panel output that solar output varies significantly in the sub-minute time scale. Existing modeling and prediction techniques that focus on long-term low-resolution forecasting over minutes to years do not properly capture the fast dynamics of solar generation. As the percentage of total generation created by non-dispatchable generation sources increases, these short time-scale dynamics will cause large local voltage and frequency fluctuations. To counteract this, real-time tertiary dispatch controllers need to be developed. These controllers will benefit from short-term high resolution prediction of solar output. This paper presents two novel stochastic forecasting models for solar PV by utilizing historical inter-minute data to outline a short-term high-resolution probabilistic behavior of solar. First, we propose an uncertain basis functions method to forecast both solar irradiance and PV power. Three possible distributions are considered for the uncertain basis functions - Gaussian, Laplace, and Uniform distributions. Second, stochastic state-space models are proposed to characterize the behaviors of solar irradiance and PV power output. A filter-based expectation-maximization and Kalman filtering mechanism is employed to recursively estimate the parameters and states variables. This enables the system to accurately predict small as well as large fluctuations of the solar signals. The proposed forecasting models are suitable for real-time tertiary dispatch controllers and optimal power controllers. The PV forecasting models are tested using solar irradiance and PV power measurement data collected from a 13.5 kW PV panel installed on the rooftop of our laboratory. The results are compared with standard time series forecasting mechanisms and have shown a substantial improvement in the prediction accuracy of the total energy produced.